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# Number Theory

Delves into the fundamental concepts and properties of numbers, divisibility, and modular arithmetic, laying the foundation for advanced mathematical study.

## goldbach's conjecture.

-74 mod 8 = ?

• 8
• 6
• 7
• 5

Which expression has a value different from the others?

• -3 + 2 + (-4)
• (4 - 3) - 4
• -11 - 4 + 12
• 3- 2 - 4

Which of the following numbers below is the answer to 43 modulo 5?

• 5
• 8
• 3
• 7

Complete the expression =E2=80=9953 = 125 = 14 (mod ___ )=E2=80=99

• 33
• 37
• 38
• 43

Which expression has the greatest value?

• 3 + (-2)
• (-3+4) (-1)
• -3 + 3
• 3 + (-4)

Which of the following prime numbers below is a Mersenne Prime?

• 89
• 127
• 23
• 13

Using Euclidean Algorithm, determine the remainder of 8 420 and 3 020

• 23
• 20
• 17
• 7

If the integers 5, 3, -4, 7, -10, 8, and -5 are arranged in order from least to greatest which integer would come first in the list.

• 8
• 3
• -10
• -4

The numbers 2, 2, 2, 3, 3, 5, 7, and 11 are the factors of what number?

• 27,720
• 20,720
• 22,720
• 21,720

-60 mod ___ = 0

• 7
• 12
• 9
• 16

The number of multiples of 6 from 20 to 50 is ________.

• 5
• 7
• 8
• 4

4199 is divisible by 17.

• True
• False

Using the formula of Mersenne prime 2k =E2=80=93 1, if k = 11, the value is

• 2,048
• 2,047
• 2,046
• 2,049

Find the Greatest Common Divisor: 420 and 315

• 105
• 10
• 15
• 20

Write all the multiples of 7 between 5 and 50.

• 7, 15, 24, 28, 32, 38, 46
• 7, 14, 22, 26, 36,43, 49
• 7, 14, 21, 28, 35, 42, 49
• 7, 13, 18, 27, 35, 42, 48

Which of the following pairs of numbers has a remainder of 12?

• 532 and 440
• 564 and 488
• 9 324 and 7 608
• 13 685 and 495

Using Euclidean Algorithm, determine the remainder of 703 and 259

• 20
• 23
• 37
• 15

The factors of 30 in the factor tree are

• 5 and 6
• 3 and 7
• 6 and 2
• 4 and 5

4199 is divisible by 11.

• True
• False

The solution to 96 modulo 32 is _________.

• 7
• 1
• 3
• 0

The factors of the number is 25 x 32 x 37. What is the number?

• 7,104
• 5,787
• 5,328
• 10,656

From the given numbers below, _______ is the coprime of 143.

• None of the choices
• 13
• 19
• 11

Find TWO common multiples of the given numbers: 2 and 5

• 15 and 30
• 5 and 15
• 10 and 20
• 20 and 25

Listed below are three numbers that are composite. Which is not?

• 681
• 878
• 577
• 785

The primitive roots of mod 55 using coprimes 5, 7, and 11 using base 3 are 23, 42, and ____.

• 45
• 49
• 47
• 51

The following are the quadratic residue of modulo 27 , EXCEPT

• 8
• 7
• 3
• 4

4199 is divisible by 23.

• True
• False

The expressions below have a solution of 10.

• 78 mod 17
• 45 mod 23
• 72 mod 15
• 33 mod 21

Find the Greatest Common Divisor. Apply any method: 244 and 260

• 6
• 2
• 4
• 8

Using Euclidean Algorithm, determine the remainder of 18476 and 2636

• 4
• 10
• 23
• 15

The following pairs below shows an example of fundamental theorem of arithmetic, EXCEPT:

• 17 x 19
• 7 x 41
• 9 x 11
• 11 x 3

_________ is defined as the remainder of the bn less the modulo.

• Power Function
• Congruence Modulo
• Power Modulo
• Primitive Roots

If a number is divisible by 23, multiply the last digit of the given number to 7 and add the remaining number. Repeat the steps if necessary.

• True
• False

Which of the following expressions below is INCORRECT?

• 21 mod 6 = 3
• 82 mod 7 = 5
• 42 mod 2 = 2
• 100 mod 8 = 4

If a number is divisible by 43, multiply 13 to the last digit of the number and add to the remaining number. Repeat steps if necessary.

• True
• False

The following numbers are coprime of 34, EXCEPT:

• Non of the choices
• 13
• 2
• 7

Which of the following is a prime number?

• 1
• 221
• 101
• 201

The following are the other quadratic residues of modulo 28, EXCEPT:

• 4
• 8
• 1
• 13

The number of divisor of a certain integer is being added.

• True
• False

Which of the following is the prime factorization of 328?

• 23 x 41
• 33 x 41
• 22 x 41
• 32 x 41

If you substitute 5 to the Fermat form, the answer is ________?

• 32
• 31
• 11
• 33

Find the Greatest Common Divisor. Apply any method: 366 and 420

• 4
• 6
• 2
• 3

Which of the following is the prime factor of 81, 141?

• 31
• 43
• 21
• 19

How many factors does 421 have?

• 2
• 3
• 4
• 5

Which list below are the numbers arranged in order from greatest to smallest?

• 5, 4, 0, -3
• -5, -4, -3, -2, -1,
• 1, 3, 5, 7, 10,
• 2, 4, 6, 8, 10,

What must be the missing value of the expression to make it ? 76 = 117 649 = ___ (mod 3)

• 1

In finding the answer in 59 mod 5, the usual last step of congruence modulo is

• The remainder is the answer
• Divide 59 and 5
• Multiply the whole number to 5
• Subtract the product to the first whole number

The following are sets of integers, EXCEPT

• { 05, 1/3,}
• {-2, -5, -7,=E2=80=A6}
• {1, 2, 3,=E2=80=A6}
• {-3, -5, -7,=E2=80=A6}

1890 is divisible by 3.

• True
• False

Using Euclidean Algorithm, determine the remainder of 1541 and 897

• 23
• 15
• 37
• 20

Find the Greatest Common Divisor: 469 and 357

• 3
• 9
• 14
• 7

Find the Greatest Common Divisor. Apply any method: 125 and 275

• 25
• 10
• 15
• 5

Using the formula of Mersenne prime 2d =E2=80=93 1, if d = 17, the value is

• 131 075
• 131 071
• 131 072
• 131 073

What is the primitive root of mod 75 using 7 as one of its coprimes?

• 25
• 43
• 33
• 37

The following pairs of numbers has a GCD of 31, EXCEPT:

• 6750 & 1519
• 2573 & 2759
• None of the choices
• 1519 & 2573

The missing value of the expression 39 = 19 683 = 6 (mod __).

• 5
• 9
• 3
• 7

Which of the following pairs of numbers has a remainder of 5?

• 16, 476 and 636
• 18, 477 and 838
• 16, 475 and 643
• 13 865 and 495

Which of the following numbers below is the GCD of 48 and 60?

• 6
• 12
• 16
• 4

Find the Least Common Multiple: 2 and 3

• 16
• 6
• 9
• 10

The symbol sigma is used to determine the sum of the given objects.

• True
• False

What are the unknown numbers in the factor tree?

• 2 and 18
• 3 and 12
• 1 and 36
• 4 and 9

Complete the statement: 152 = 225 = ___ (mod 27).

• 4
• 9
• 10
• 7

1890 is divisible by 9.

• True
• False

What must be the value of the unknown if, 112 = 121 = ___ (mod 28)?

• 10
• 12
• 9
• 11

Find the Greatest Common Divisor: 77 and 121

• 21
• 11
• 1
• 22

The prime factors of 420 are 2, 3, 5 and ____.

• 13
• 7
• 19
• 11

-119 mod 16 = ?

• 9
• 11
• 8
• 7

Using Euclidean Algorithm, determine the remainder of 1 515 and 705

• 37
• 20
• 15
• 23

The rules in obtaining the divisibility of 3 is

• If a number starts 3, 6, or 9
• If a number ends in 3, 6 or 9
• If the last two digits of the given number is divisible by 3
• Add all the digits of the given number

Which of the following is the correct way to write the set notation of factors of 56?

• {56, 28, 14, 8, 7, 4, 2, 1}
• {1, 2, 4, 7, 8, 14, 28, 56}
• {1, 56, 2, 28, 4, 14, 7, 8}
• {56, 27, 14, 9, 7, 3, 2, 1}

The LCM of 2, 3, and 6 is _______.

• 8
• 12
• 2
• 6

If k is less than 0 where k is not an integer, then f(0) is undefined and it has no y-intercepts.

• True
• False

Which of the following numbers is divisible by 47?

• 11,549
• 12,549
• 10,549
• 9,549

Which of the following is the quadratic non residue of modulo 27?

• 13
• 11
• 9
• 10

4199 is divisible by 19.

• True
• False

Find the Greatest Common Divisor: 352 and 41

• 1
• irregularly prime
• coprime
• 2

The following are the divisors of 60, EXCEPT:

• 12
• 18
• 15
• 3

Write all the multiples of 12 between 20 and 150

• 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144
• 12, 36, 46, 60, 72, 83, 96, 108, 120, 132, 144
• 12, 24, 48, 60, 72, 84, 96, 108, 120, 132, 144
• 24, 36, 48, 60, 72, 83, 96, 108, 120, 132, 144

Based on the given factor tree, what is the unknown number?

• 315
• 135
• 351
• 153

Which of the following are the prime factors of 360?

• 23 x 33 x 5
• 23 x 32 x 5
• 22 x 32 x 5
• 23 x 34 x 5

What is the value of f(x) = 2xk, if k = 2.

• 2x2
• 2xk
• 2(2)k
• 2x(k)(2)

An exponential function has a fixed base that is raised to a variable.

• True
• False

In a power function the base is a variable and raised to a fixed exponent.

• True
• False

Find the Least Common Multiple: 3 and 11

• 44
• 22
• 33
• 55

-94 mod ____ = 8

• 15
• 17
• 12
• 13

=E2=80=9CIf a number is divisible by _________, multiply 3 to the last digit then add the remaining number. Repeat the steps if necessary.=E2=80=9D This rule applies in

• Divisibility of 29
• Divisibility of 17
• Divisibility of 19
• Divisibility of 23

Given: 162 = 256 = ___ (mod 27), what must be the value of the unknown?

• 13
• 14
• 12
• 15

Find the Greatest Common Divisor. Apply any method: 3425 and 4520

• 5
• 15
• 25
• 10

Write all the multiples of 6 between 4 and 40.

• 6, 12, 18, 24, 30, 36
• 6, 12, 17, 24, 30, 38
• 6, 12, 18, 24, 32, 39
• 6, 10, 14, 18, 26, 37

What is the primitive root of mod 75 using 7 as one of its coprime?

• 43
• 16
• 37
• 25

Which of the following numbers below is divisible by 2, 3, 5, and 7?

• 5,989
• 12,358
• 24,350
• 10,500

The factors of 270 with the most times repeated is

• 3
• 7
• 5
• 2

Find the Least Common Multiple: 4, 8 and 10

• 65
• 30
• 40
• 60

A power function has a fixed __________.

• exponent
• base
• form
• None of the choices

The following expressions are correct, EXCEPT:

• None of the choices

Which of the following pairs of numbers has a remainder of 2?

• 5 126 and 1 512
• 756 and 272
• 13 865 and 495
• 603 and 359

The numbers below are the common factors of 30 and 45, EXCEPT:

• 15
• 5
• 3
• 10

How many primitive roots below 100 does 421 have if the coprimes are between 5 and 11, using 3 as base?

• 3
• 0
• 2
• 1

What must be the value of the missing value of the expression 213 = 8 192 = 2 (mod __ ) to make it correct?

• 11
• 7
• 5
• 9

Find the Greatest Common Divisor: 976 and 696

• 4
• 8
• 2
• 3

The factors of 300 are the prime numbers 2, 3 and 5. Which of the following numbers appears twice?

• 2 and 3
• 2 and 5
• 2, 3 and 5
• 3 and 5

If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.

• True
• False

Complete the expression =E2=80=9927 = 128 = ___ (mod 63)=E2=80=99

• 4
• 3
• 2
• 5

75 mod 6 = ?

• 5
• 2
• 3
• 1

Find the Greatest Common Divisor: 36 and 99

• 9
• 12
• 18
• 3

IF a number is divisible by _________, multiply 3 to the last digit then add the remaining number Repeat the steps if necessary This rule applies in

• Divisibility of 29

Which of the following are the prime factors of 3024?

• 24 x 32
• 7 x 8 x 9 x 12
• 7 x 24 x 33
• 6 x 7 x 8 x 9

24 mod 3 = ?

• 1
• 3
• 4
• 0

88 mod 9 = ?

• 6
• 7
• 9
• 8

Find the Greatest Common Divisor. Apply any method: 1800 and 2300

• 50
• 200
• 300
• 100

25 mod 5 = ?

• 5
• 0
• 1
• 3

What must be the value of g, in the formula 2g =E2=80=93 1 = 8 191, to make it correct?

• 11
• 17
• 13
• 7

The primitive root of mod 60 using 11 as one of the primitive roots is

• 1
• 11
• 3
• 2

Complete the expression '53 = 125 = 14 (mod ___ )'

• 37

Which of the following number below is a Mersenne Prime?

• 31
• 13
• 7
• 23

The following are the multiples of 12 between 120 and 450, EXCEPT?

• 270
• 432
• 362
• 182

Write all the multiples of 8 between 3 and 100.

• 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
• 8, 16, 24, 32, 40, 48, 54, 64, 72, 80, 88, 96
• 8, 16, 24, 32, 40, 48, 54, 63, 72, 80, 88, 96
• 8, 16, 24, 32, 40, 46, 56, 64, 72, 80, 88, 97

Which of the following is the solution of the expression 23 x 52 x 7?

• 2400
• 1400
• 1700
• 2100

-60 mod 3 = ?

• 2
• 0
• 3
• -1

Complete the statement: 252 = 625 = ___ (mod 28).

• 11
• 9
• 7
• 5

The _____________ is the modulo of a certain number.

• remainder
• sum
• difference
• product

What must be the value of the last digit of 23, 31__ to make it divisible by 5?

• 0
• 8
• 4
• 7

Find TWO common multiples of the given numbers: 4 and 5

• 20 and 30
• 10 and 20
• 15 and 40
• 20 and 40

What must be the value of the unknown if, 182 = 324 = ___ (mod 27)?

• 3
• 2
• 1
• 0

____ mod 9 = 5

• 23
• 74
• -12
• 13

Find the Greatest Common Divisor. Apply any method: 500, 600 and 700

• 150
• 50
• 10
• 100

What is the greatest common factor of 36 848 and 77 080?

• 94
• 188
• 376
• 88

The GCD of 90 and 105 is ________.

• 3
• 5
• 18
• 15

The Fermat form is in the form __________.

• 2s - 1
• 2s + 1

Find TWO common multiples of the given numbers: 8 and 9

• 32 and 72
• 72 and 144
• 56 and 64
• 54 and 144

Which of the following pair of numbers has a greatest common divisor of 159?

• 13, 685 and 490
• 5 120 and 1 510
• 14 628 and 5 565
• 9 325 and 7 608

Which of the following is the first step to find the answer in 59 mod 5?

• Multiply the whole number to 5
• The remainder is the answer
• Divide 59 and 5
• Subtract the product to the first whole number

Which solution is from the given factor tree below?

• i and ii

Which of the following pairs of numbers shows a fundamental theorem of arithmetic?

• 23 x 27
• 21 x 48
• 89 x 97
• 37 x 49

Which of the following is the next step to find the remainder of 10,465 and 3,553?10 465 = 3 553(2) + 3 359 3 553 = 3 359(1) + 194 3 359 = 194(17) + 61

• 3 359 = 17(197) + 10
• 194 = 17(11) + 7
• 194 = 61(3) + 11
• 3 359 = 61(55) + 4

From the given numbers, which number has more number of factors?

• 25
• 45
• 15
• 30

1890 is divisible by 7.

• True
• False

Which of the following pairs of numbers has a remainder of 13?

• 1,865 and 495
• 12,865 and 595
• 5 126 and 1 512
• 650 and 273

Which of the following is the correct way to find the prime factorization of 24?

• ii only
• None of the choices
• both i and ii
• i only

Find the Least Common Multiple: 4 and 15

• 70
• 30
• 45
• 60

Which of the following numbers below is a factor that is common to 120 and 42?

• 20
• 6
• 7
• 14

The modulo of a certain number is obtained by

• division
• multiplication
• subtraction

Find the Greatest Common Divisor: 624 and 516

• 12
• 2
• 3
• 9

What is the remainder if you apply the Euclidean Algorithm to 10 465 and 3 553?

• 3
• 2
• 0
• 1

Find the Greatest Common Divisor. Apply any method: 899 and 760

• prime
• 6
• relatively prime or coprime
• 8

Find the Least Common Multiple: 2 and 7

• 35
• 21
• 14
• 10

Which of the following are the prime factors of 234?

• 2 x 3 x 132
• 2 x 3 x 13
• 22 x 3 x 13
• 2 x 32 x 13

129 mod 13 = ?

• 10
• 7
• 12
• 11

Given: 22 = 4 = 32 (mod ___), what must be the value of the unknown?

• 26
• 28
• 22
• 24

Find the Least Common Multiple: 6 and 14

• 56
• 42
• 49
• 28

The expressions below are all correct, EXCEPT:

• 53 = 125 = 10 (mod 15)
• 39 = 19 683 = 48 (mod 55)
• 24 = 16 = 7(mod 9)
• 25 = 32 = 4 (mod 7)

Find the Greatest Common Divisor: 210 and 320

• 10
• 5
• 2
• 20

The expressions below are all , EXCEPT:

• 53 = 125 = 10 (mod 15)

Find the Least Common Multiple: 4, 6 and 8

• 28
• 32
• 16
• 24

Complete the expression =E2=80=98 __13 = 1,594,323 = 819 (mod 1584)=E2=80=99

• 5
• 2
• 4
• 3

If we substitute 7 for s, from the formula 2s + 1, then the answer is ____.

• 128
• 135
• 129
• 50

The following are the quadratic residue of modulo 28 , EXCEPT

• 10
• 8
• 9
• 4

-46 mod 5 = ?

• 1
• -1
• 0
• 4

What is the remainder if we use Euclidean Algorithm between 55, 230 and 3, 985?

• 1
• 3
• 0
• 2

The following are the multiples of 2, 3, and 7, EXCEPT:

• 72
• 126
• 42
• 21

Describe the value k of the function f(x) = 5xk, so that the answer is a fraction?

• Fraction
• Zero
• Positive
• Negative

The following expressions are , EXCEPT:

• None of the choices

Three of the numbers below are divisible by 13, 15 and 17. Which is NOT?

• 29,835
• 33,150
• 48,645
• 62, 985

If a number is divisible by 37, multiply 11 to the last digit minus the remaining number. Repeat the steps if necessary.

• True
• False

Find the Greatest Common Divisor: 265 and 190

• 25
• 5
• 15
• 10

Which of the following expressions is correct?

• None of the choices

Complete the expression =E2=80=98 __13 = 1,594,323 = 819 (mod 1584)=E2=80=99.

• 7
• 2
• 3
• 5

Power function is presented in the form f(x) = abc.

• True
• False

Which of the following is the way to find the prime factorization of 24?

• both i and ii

The value of p in the expression 2p =E2=80=93 1 = 524 287 is ______.

• 29
• 21
• 17
• 19

If you obtain the factors of 444, the largest prime number is

• 23
• 11
• 37
• 3

-35 mod 7 = ?

• 4
• 3
• 0
• 1

All numbers below are divisible by 3 except

• 5783
• 9102
• 7562
• 4704

The factors of 355 are ____ numbers.

• 4
• 2
• 5
• 3

The factors of 12 from the given factor tree are 3 and ____.

• 2
• 4
• 3
• 6

The price of gasoline decline Php 140 over a one week period. If the rate decrease was spread equally over the week, how much did the price of gasoline decrease in one day?

• Php 1600
• Php 2000
• pHP 2300
• Php 2800

What must be the missing value of the expression to make it correct? 76 = 117 649 = ___ (mod 3)

• 3
• 1
• 0
• 2

4199 is divisible by 13.

• True
• False

Find the Least Common Multiple: 3 and 7

• 28
• 18
• 35
• 21

Which among the numbers below is equal to 38 mod 9?

• 4
• 2
• 3
• 7

If we substitute 7 for s, from the formula 2s + 1, then the answer is ____. Is the answer a Fermat number?

• Maybe
• No
• Yes

Given: 202 = 400 = 22 (mod ___), what must be the value of the unknown?

• 17
• 23
• 15
• 27

Which of the following is a coprime of 483?

• 5
• 7
• 3
• 21

The numbers below are coprime, EXCEPT:

• 23 and 54
• 3 and 42
• 1 and 27
• 100 and 99

-87 mod 6 = ?

• 4
• 3
• 1
• 2

Double the last digit of the given number and subtract it from the remaining number excluding the last digit. This rule applies in

• Divisibility by 4
• Divisibility by 7
• Divisibility by 3
• Divisibility by 11

83 mod 7 = ?

• 3
• 9
• 6
• 7

If a number is divisible by 47, multiply 14 to the last digit of the number and add from the remaining number. Repeat the steps if necessary.

• True
• False

Which solution is correct from the given factor tree below?

• None of the choices
• i only
• ii only
• i and ii

The following are the multiples of 3 and 5, EXCEPT:

• {30, 60, 90,=E2=80=A6}
• {3, 6, 9,=E2=80=A6 5, 10,=E2=80=A6}
• {15, 30, 45,=E2=80=A6}
• {3, 7, 9,=E2=80=A6 5, 10,=E2=80=A6}

If you substitute a negative integer to the exponent of a power function, then the answer is _____________.

• singularity
• symmetry
• none of the choices
• anti-symmetry

Which of the following form shows a power function?

• f(x) = 2xk
• f(x) = -3xk
• f(x) = 3xk
• f(x) = -xk

42 mod 5 = ?

• 2
• 3
• 5
• 8

The solution of the statement 231 =E2=80=93 1 = ____.

• 2 147 483 646
• 2 147 483 648
• 2 147 483 647
• 2 147 483 649

If the values of k are odd integers, thus the function has a certain symmetry.

• True
• False

Find the Greatest Common Divisor: 138 and 224

• 3
• 1
• 4
• 2

Find TWO common multiples of the given numbers: 3 and 4

• 12 and 16
• 8 and 12
• 12 and 24
• 15 and 21

-78 mod 8 = ?

• 2
• 4
• 1
• 0

Which of the following numbers below is the LCM of 7 and 10?

• 7
• 140
• 28
• 70

All numbers are coprime of 385, EXCEPT:

• 3
• 13
• 5
• 2

The least common multiple of 9 and 12 is __________.

• 12
• 27
• 36
• 18

Find the Least Common Multiple: 10, 12 and 15

• 60
• 45
• 70
• 65

The largest factor of 279 is

• 23
• 31
• 29
• 19

Using s = 2, in the Fermat formula 2s + 1, is the answer a Fermat number?

• Maybe
• No
• Yes

How many divisors does 12 have?

• 8
• 4
• 6
• 10

Find the Greatest Common Divisor. Apply any method: 4250 and 2530

• 15
• 30
• 5
• 10

Which of the following is a coprime of 385?

• Non of the choices
• 7
• 3
• 5

What is the value of 216 + 1? Is it a Fermat Number?

• 65, 537 No, it is not a Fermat Number
• 65, 536 No, it is not a Fermat Number
• 65, 536 Yes, it is a Fermat Number
• 65, 537 Yes, it is a Fermat Number

All numbers are divisible by 1.

• True
• False

1890 is divisible by 5.

• True
• False

The expressions below have a solution of 12, EXCEPT:

• 78 mod 17
• 47 mod 35
• 33 mod 21
• 72 mod 15

Which of the following is the LCM of 12 and 15?

• 120
• 90
• 60
• 240

Which of the following expressions is below is correct?

• 25 mod 4 = 2
• 22 mod 6 = 2
• 24 mod 7 = 4
• 23 mod 5 = 3

Which of the following pairs of numbers has a remainder of 8?

• 536 and 488
• 5 126 and 1 512
• 650 and 273
• 3,541 and 897

Using the function f(x) = -xk, if x = 0 and k is a negative integer then it is an example of singularity.

• True
• False

What is the product of the prime factors 2,2 and 53?

• 106
• 49
• 57
• 212

Base on the given factor tree, what numbers should be written inside the boxes?

• 2 and 3
• 3 and 5
• 3 and 4
• 2 and 2

Write all the multiples of 17 between 70 and 160.

• 85, 102, 119, 136, 153
• 85, 102, 119, 135, 153
• 85, 104, 119, 138, 153
• 85, 103, 119, 137, 153

The following are the numbers you can multiply to produce the fundamental theorem of arithmetic, EXCEPT:

• 53, 59, 61, 67, 71, 73
• 3, 5, 7, 11, 13, 17
• 31, 37, 41, 43, 47, 49, 51
• 3, 37, 61, 71, 73

35 modulo 7 = ?

• 0
• 2
• 3
• 5

Complete the mathematical statement: 22^2 = ____ = 25 (mod 27).

• 484
• 361
• 400
• 441

The following numbers are all Fermat numbers, EXCEPT:

• 2
• 5
• 3
• None of the choices

What must be the value of the unknown if, ___ = 64 = 10 (mod 27)?

• 83
• 43
• 26
• 82

A Fermat Number is a prime number that follows the form of 2s + 1.

• True
• False

Which of the following is the quadratic non residue of modulo 28?

• 13
• 16
• 20
• 18

The number with the most numbers of multiples between 5 and 35 below is _________.

• 8
• 6
• 4
• 7

The following are the factors of 72, EXCEPT:

• 12
• 8
• 6
• 23

All of the numbers below have an answer of 4, EXCEPT:

• 95 mod 7
• 76 mod 9
• 64 mod 6
• 73 mod 8

Complete the expression '27 = 128 = ___ (mod 63)'

• 2

Which of the following operations results in a difference?

• Division
• Multiplication
• Subtraction

The greatest common divisor of 19,342 and 2,766 is ______.

• 3
• 2
• 6
• 8

The factors of 14 in the factor tree are 7 and ____.

• 3
• 4
• 2
• 5

If a number is divisible by 11, the last 3 digits must be divisible by 11.

• True
• False

The following are the primitive roots of mod 50 base 2, EXCEPT:

• 12
• 5
• 14
• 28

Which of the following is the way to write the set notation of factors of 56?

• {1, 2, 4, 7, 8, 14, 28, 56}

The Greek letter t is used in finding the divisor function.

• True
• False

Simplify the expression 32 x 52 x 7 = ?

• 1575
• 1225
• 1455
• 1305

In mod 33, using 2, 3, and 5 as coprimes and base 5, the primitive roots are 8, ____, and ____.

• 21 and 23
• 23 and 25
• 25 and 26
• 23 and 26

What is the remainder of 23 069 and 20 069 when you use the Euclidean Algorithm?

• 3
• 1
• 0
• 2

Using the Mersenne Primes, if you apply 23, the value is ______.

• 8,388,607
• 16,777,215
• 7, 787, 300
• 4,194,303

What must be the value k to make the function f(x) = -3xk equal to -3?

• -1
• 1
• 0

Which of the following pairs of numbers below have the LEAST number of common multiples from 1 to 30?

• 3 and 5
• 2 and 3
• 2 and 5
• 4 and 5

Using the Fermat number 2s + 1, find the value using s = 2.

• 3
• 7
• 9
• 5

Which of the following numbers that can be presented using exponents in factorization?

• 8972
• 3570
• 7567
• 5184

The following are the quadratic non residue of modulo 27, EXCEPT

• 16
• 14
• 15
• 17

From the given numbers below, _______ is the coprime of 286?

• 19
• 2
• 13
• 11

37 mod 4 = ?

• 1
• 0
• 3
• 4

Find the Least Common Multiple: 5 and 7

• 25
• 70
• 45
• 35

The following are the other quadratic residues of modulo 28 , EXCEPT

• 21
• 25
• 27
• 20

What must be the value of the last digit of 3, 45__ to make it divisible by 8?

• 0
• 6
• 16
• 8

If one of the factor of 420 is 14, the other one is____.

• 30
• 28
• 20
• 23

Johnny borrowed money from his brother 10 months ago. He returned Php 1000.00 per month to his brother starting the month he borrowed the money. Currently, he owes his brother Php 5,000.00. How much money did he borrow from his brother?

• Php 20,000
• Php 15,000
• Php 10,000
• Php 12,000

Which of the following pairs of numbers below shows the properties of relatively prime?

• 99 and 100
• 63 and 21
• 2 and 36
• 15 and 90

What is the value of the expression -5 + 5 + (-12)?

• -22
• 22
• -2
• -12

Find TWO common multiples of the given numbers: 5 and 11

• 5 and 55
• 5 and 33
• 55 and 110
• 55 and 125

What are the primitive roots of mod 209 using coprimes 7, 11, and 13 and base 2?

• 41, 82 and 167
• 41, 81 and 167
• 67, 113 and 205
• 82, 178 and 327

The following are the quadratic non residue of modulo 28, EXCEPT

• 25
• 23
• 22
• 24

A number is divisible by 2 and 3. Thus it is also divisible by 6.

• True
• False

1890 is divisible by 2.

• True
• False

Find the Greatest Common Divisor. Apply any method: 178 and 150

• 6
• 8
• 4
• 2

Using Prime Factorization, what is the value of 23 x 32 x 5 x 11?

• 2850
• 3570
• 3960
• 4130

What must be the value of the unknown if, ___ = 36 = 8 (mod 28)?

• 361
• 62
• 9 x 4
• 3 x 12

Complete the mathematical statement: 142 = ____ = 0 (mod 28)

• 189
• 169
• 144
• 196

Find the Greatest Common Divisor. Apply any method: 78 and 96

• 2
• 6
• 3
• 4

If a number is divisible by 31, multiply the last number to 3 and subtract from the remaining number. Repeat the steps if necessary.

• True
• False

The primitive root of mod 60 using 11 as one of the primitive root is

• 4
• 7
• 11
• 2

What is the GCD of 108 and 81?

• 27
• 12
• 29
• 9

What must be the last digit of a number to make it divisible by 10?

• 2
• 5
• 0
• 1
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Euclidean Algorithm

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