Basics of Congruence

  • 9th Grade
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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: 11 | Questions: 10 | Updated: Jan 20, 2026
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1) Which statement is true?

Explanation

17=7×2+3 → remainder 3.

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About This Quiz
Basics Of Congruence - Quiz

What does it mean when two numbers are “congruent” to each other? In this quiz, you’ll explore the idea of congruence, practice writing and checking statements like a ≡ b (mod n), and see how simple it is to spot when numbers share the same remainder. Take this quiz to... see moreget started with the building blocks of modular congruence.
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2)

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2) Which is equivalent to 25 ≡ ? (mod 6)

Explanation

25=6×4+1.

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3) If 42 ≡ r (mod 8), what is r?

Explanation

42=8×5+2.

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4) Which of the following congruences is correct?

Explanation

19=9×2+1.

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5) Which pair of numbers are congruent mod 5?

Explanation

27≡2, 32≡2 (mod 5).

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6) If x ≡ 4 (mod 6), which number could x be?

Explanation

Numbers of form 6k+46k+46k+4: 4, 10, 16, …

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7) Which congruence is true?

Explanation

50=9×5+5.

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8) Which is correct about 33 mod 11?

Explanation

33 is a multiple of 11.

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9) If a ≡ 2 (mod 7), what is a + 7?

Explanation

Adding 7 (a multiple of 7) doesn’t change the congruence class.

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10) Which of the following is equivalent to 71 mod 10?

Explanation

71=10×7+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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Which statement is true?
Which is equivalent to 25 ≡ ? (mod 6)
If 42 ≡ r (mod 8), what is r?
Which of the following congruences is correct?
Which pair of numbers are congruent mod 5?
If x ≡ 4 (mod 6), which number could x be?
Which congruence is true?
Which is correct about 33 mod 11?
If a ≡ 2 (mod 7), what is a + 7?
Which of the following is equivalent to 71 mod 10?
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