Basics of Modular Multiplication

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 13 | Questions: 10 | Updated: Dec 9, 2025
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1) Find 6 × 7 (mod 8).

Explanation

6 × 7 = 42. Divide by 8 → remainder 2.

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About This Quiz
Basics Of Modular Multiplication - Quiz

Modular multiplication can look tricky, but it’s really about working with remainders after multiplication. In this quiz, you’ll start with simple problems that show how multiplying numbers and then reducing them “mod n” gives neat, repeatable results. Take this quiz to build a solid foundation in modular math.

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2) Find 15 × 11 (mod 10).

Explanation

15 × 11 = 165. Divide by 10 → remainder 5.

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3) Compute 8 × 7 (mod 12).

Explanation

8 × 7 = 56. Divide by 12 → remainder 8.

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4) Compute 3 × 4 (mod 5).

Explanation

3 × 4 = 12. Dividing by 5 leaves remainder 2.

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5) What is 9 × 5 (mod 7)?

Explanation

9 × 5 = 45. Divide by 7 → remainder 3.

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6) Compute 12 × 6 (mod 9).

Explanation

12 × 6 = 72. Divide by 9 → remainder 0.

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7) Find 14 × 9 (mod 5).

Explanation

14 × 9 = 126. Divide by 5 → remainder 1.

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8) Compute 25 × 6 (mod 7).

Explanation

25 × 6 = 150. Divide by 7 → remainder 3.

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9) Find 10 × 10 (mod 9).

Explanation

10 × 10 = 100. Divide by 9 → remainder 1.

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10) Compute 21 × 13 (mod 8).

Explanation

21 × 13 = 273. Divide by 8 → remainder 1.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Find 6 × 7 (mod 8).
Find 15 × 11 (mod 10).
Compute 8 × 7 (mod 12).
Compute 3 × 4 (mod 5).
What is 9 × 5 (mod 7)?
Compute 12 × 6 (mod 9).
Find 14 × 9 (mod 5).
Compute 25 × 6 (mod 7).
Find 10 × 10 (mod 9).
Compute 21 × 13 (mod 8).
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