Understanding Modular Inverses

  • 9th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
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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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Quizzes Created: 8157 | Total Attempts: 9,569,759
| Attempts: 11 | Questions: 10 | Updated: Dec 9, 2025
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Question 1 / 11
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1) Which number is the inverse of 3 mod 7?

Explanation

3 × 5 = 15; 15 mod 7 = 1. So the inverse is 5.

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About This Quiz
Understanding Modular Inverses - Quiz

In this quiz, you’ll explore what it means for a number to have a modular inverse and when an inverse exists. You’ll test simple cases, practice checking whether numbers are invertible, and see how multiplication “wraps around” under modular arithmetic. Take this quiz to build your first steps in mastering... see moreinverses.
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2) Find the modular inverse of 2 mod 5.

Explanation

2 × 3 = 6; 6 mod 5 = 1. So the inverse is 3.

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3) What is the inverse of 4 mod 7?

Explanation

4 × 2 = 8; 8 mod 7 = 1. So the inverse is 2.

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4) Which number is the inverse of 5 mod 11?

Explanation

5 × 9 = 45; 45 mod 11 = 1. So the inverse is 9.

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5) Which number is the inverse of 7 mod 10?

Explanation

7 × 3 = 21; 21 mod 10 = 1. So the inverse is 3.

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6) What is the modular inverse of 6 mod 17?

Explanation

6 × 3 = 18; 18 mod 17 = 1. So the inverse is 3.

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7) Which has no inverse?

Explanation

gcd(6,9) = 3 ≠ 1 → no inverse.

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8) If x is the inverse of 4 mod 9, then 4x ≡ 1 (mod 9). Which is x?

Explanation

4 × 7 = 28; 28 mod 9 = 1. So x = 7.

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9) Which number is the inverse of 11 mod 26?

Explanation

11 × 19 = 209; 209 mod 26 = 1. So the inverse is 19.

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10) Which number is the inverse of 8 mod 15?

Explanation

8 × 2 = 16; 16 mod 15 = 1. So the inverse is 2.

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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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Which number is the inverse of 3 mod 7?
Find the modular inverse of 2 mod 5.
What is the inverse of 4 mod 7?
Which number is the inverse of 5 mod 11?
Which number is the inverse of 7 mod 10?
What is the modular inverse of 6 mod 17?
Which has no inverse?
If x is the inverse of 4 mod 9, then 4x ≡ 1 (mod 9). Which is x?
Which number is the inverse of 11 mod 26?
Which number is the inverse of 8 mod 15?
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