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CTET Divisibility Rule — practice questions

Explore 58 free Divisibility Rule questions in CTET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Divisibility Rule questions and exercises with answers

Showing questions 1–30 of 58.

Which single digit of a number decides if it is divisible by 2?Read the answer and worked solution →Divisibility by 3 depends on whether which quantity is a multiple of 3?Read the answer and worked solution →Adding the digits of 492 gives which sum for the test of 3?Read the answer and worked solution →Pick the number whose digits add up to a multiple of 9.Read the answer and worked solution →For testing 4, which ending part of the number is examined?Read the answer and worked solution →Why do only the last two digits matter when testing for 4?Read the answer and worked solution →Which number has a two-digit ending that is a multiple of 4?Read the answer and worked solution →Another way to test 4 is to halve the number. What must be true of the half?Read the answer and worked solution →A number divisible by 5 must end in which digits?Read the answer and worked solution →A shopkeeper counts 475 pencils in packs of 5. Do they divide into whole packs?Read the answer and worked solution →A number ends in 5. Drop that 5, double the rest, add 1. What does this give for 85?Read the answer and worked solution →Which pair of passed tests proves a number is a multiple of 6?Read the answer and worked solution →In the subtract-twice test for 7, you subtract twice the last digit from what?Read the answer and worked solution →Test 91 for 7: remove the last digit 1, then subtract twice it from 9. What is the result?Read the answer and worked solution →Another test for 7 adds five times the last digit to the rest. For 91, what is that total?Read the answer and worked solution →Which kind of sum is used to test divisibility by 11?Read the answer and worked solution →Using alternating digit sums, which number is divisible by 11?Read the answer and worked solution →To prove a number is divisible by 36, which pair of divisibility tests is enough?Read the answer and worked solution →To test a number for 8, which is 2 cubed, how many ending digits need checking?Read the answer and worked solution →How is a prime number characterised among numbers above 1?Read the answer and worked solution →A natural number greater than 1 that is not prime is called what?Read the answer and worked solution →Why is 5 prime but 4 is not?Read the answer and worked solution →A composite number always has at least one divisor besides which two?Read the answer and worked solution →Every positive integer is composite, prime, or which special number?Read the answer and worked solution →Which pair of primes multiplies to give the composite number 299?Read the answer and worked solution →Which is the prime factorization of 360?Read the answer and worked solution →Every composite number can be written as a product of what?Read the answer and worked solution →A composite number with exactly two prime factors is called what?Read the answer and worked solution →Who showed around 300 BC that there are infinitely many primes?Read the answer and worked solution →What does Goldbach's conjecture say about even integers above 2?Read the answer and worked solution →

Worked practice questions

Which single digit of a number decides if it is divisible by 2?

  1. The first digit
  2. The last digit
  3. The middle digit
  4. The digit sum
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Correct answer: B. The last digit

1. A number is divisible by 2 when its last digit is divisible by 2. 2. Example: 376 ends in 6, and 6 / 2 = 3, so 376 is divisible by 2. 3. The first or middle digits only change multiples of 10 or more, and 10 is already a multiple of 2, so they cannot decide it. _Source: Wikipedia, Divisibility rule, section Divisibility by 2_

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Divisibility by 3 depends on whether which quantity is a multiple of 3?

  1. Its last digit
  2. Its digit sum
  3. Its last two digits
  4. Its first digit
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Correct answer: B. Its digit sum

1. Add up every digit of the number. 2. The number is divisible by 3 if and only if that sum is divisible by 3 (the same works for 9). 3. The last digit or last two digits are used for 2, 4 and 5, not for 3. _Source: Wikipedia, Divisibility rule, section Divisibility by 3 or 9_

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Adding the digits of 492 gives which sum for the test of 3?

  1. 13
  2. 14
  3. 15
  4. 16
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Correct answer: C. 15

1. Add each digit: 4 + 9 + 2. 2. This equals 15, and 15 is divisible by 3. 3. So 492 is divisible by 3 (492 / 3 = 164). The other sums come from adding wrongly. _Source: Wikipedia, Divisibility rule, section Divisibility by 3 or 9_

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