Timedora
Free Practice Quiz Question List

Modulo, Remainders, and Congruence Online Quiz Questions

Use this free practice quiz with 20 questions to review Modulo, Remainders, and Congruence, test your knowledge, and prepare for your next test or exam.

20 questions
01
Choose one
1 point

What is 58 mod 9?

  1. A

    2

  2. B

    4

  3. C

    5

  4. D

    6

02
Choose one
1 point

Which statement correctly describes the relationship between 46 and 11 modulo 7?

  1. A

    46 is congruent to 11 modulo 7.

  2. B

    46 is congruent to 11 modulo 5.

  3. C

    46 is equal to 11.

  4. D

    46 has remainder 6 modulo 7.

03
Choose one
1 point

What is the remainder when 37 × 22 is divided by 5?

  1. A

    0

  2. B

    1

  3. C

    2

  4. D

    4

04
Choose all
1 point

Suppose x is congruent to 5 modulo 6. Select all statements that must be true.

  1. A

    x leaves remainder 5 when divided by 6.

  2. B

    6 divides x − 5.

  3. C

    x can be written as 6k + 5 for some whole-number k.

  4. D

    x must equal 5 as an ordinary number.

05
True or false
1 point

True or false: 72 mod 9 equals 0.

  1. A

    True

  2. B

    False

06
True or false
1 point

True or false: 29² is congruent to 1 modulo 6.

  1. A

    True

  2. B

    False

07
Written response
1 point

What is 314 mod 11? Enter the remainder as a whole number.

08
Written response
1 point

What is the greatest possible remainder when a positive integer is divided by 12? Enter the value as a whole number.

09
Fill in the blank
1 point

Complete the division statement: 83 = 9 × + . The first blank is the quotient, and the second blank is the remainder.

10
Fill in the blank
1 point

Complete the justification: 19 is congruent to 4 modulo 5 because 19 − 4 = , which is divisible by .

11
Open ended
1 point

Find the remainder when 47 × 26 is divided by 9. Explain how replacing each factor by a smaller congruent number makes the calculation easier.

12
Choose one
1 point

What is 65 mod 8?

  1. A

    1

  2. B

    2

  3. C

    7

  4. D

    8

13
Choose all
1 point

Select all pairs of integers that are congruent modulo 4.

  1. A

    14 and 2

  2. B

    19 and 7

  3. C

    21 and 10

  4. D

    32 and 8

14
Choose one
1 point

What is 58 modulo 9?

  1. A

    2

  2. B

    3

  3. C

    4

  4. D

    5

15
Choose one
1 point

Which list contains exactly all possible remainders when a positive integer is divided by 6?

  1. A

    1, 2, 3, 4, 5, 6

  2. B

    0, 1, 2, 3, 4, 5

  3. C

    0, 1, 2, 3, 4, 5, 6

  4. D

    0, 2, 4

16
True or false
1 point

True or false: If a modulo n equals 0, then n divides a.

  1. A

    True

  2. B

    False

17
Written response
1 point

What is the least nonnegative remainder when 73 is divided by 8? Enter the exact whole-number answer.

18
Choose one
1 point

Which statement correctly determines whether 23 is congruent to 8 modulo 5?

  1. A

    23 is not congruent to 8 modulo 5 because 23 and 8 are different

  2. B

    23 is congruent to 8 modulo 5 only if both numbers are less than 5

  3. C

    23 is congruent to 8 modulo 5 because their sum is divisible by 5

  4. D

    23 is congruent to 8 modulo 5 because their difference is divisible by 5

19
Written response
1 point

Given that x is congruent to 4 modulo 9, what is the least positive integer x greater than 20? Enter the exact whole-number answer.

20
Choose one
1 point

What is the least nonnegative remainder of 98 × 17 when divided by 5?

  1. A

    1

  2. B

    2

  3. C

    3

  4. D

    4