Divisibility rules for 2, 3, 5 and 10 worksheet

Part A: Working out and filling in

1. 1. 2

   Add the two digits you know, then think what □ must add to make the digit sum a multiple of three.

   8 + 5 + □ must be divisible by 3: trying □ from 0, the smallest is 2 (digit sum 15).

2. 2. 2

   Add the two digits you know, then think what □ must add to make the digit sum a multiple of three.

   1 + 9 + □ must be divisible by 3: trying □ from 0, the smallest is 2 (digit sum 12).

3. 3. 0

   Add the two digits you know, then think what □ must add to make the digit sum a multiple of three.

   8 + 1 + □ must be divisible by 3: trying □ from 0, the smallest is 0 (digit sum 9).

4. 4. 30, 12

   Numbers divisible by 2 are its multiples. Work out 61 ÷ 2 and look at the whole-number answer.

   Those divisible by 2 are its multiples: 61 ÷ 2 gives 30. Likewise 61 ÷ 5 gives 12.

5. 5. 38, 7

   Numbers divisible by 2 are its multiples. Work out 76 ÷ 2 and look at the whole-number answer.

   Those divisible by 2 are its multiples: 76 ÷ 2 gives 38. Likewise 76 ÷ 10 gives 7.

6. 6. 32, 19

   Numbers divisible by 3 are its multiples. Work out 96 ÷ 3 and look at the whole-number answer.

   Those divisible by 3 are its multiples: 96 ÷ 3 gives 32. Likewise 96 ÷ 5 gives 19.

Part B: Choose, or true or false

1. 7. D. 1055

   What must the last digit be for a number to divide by 5? Check each choice's last digit.

   A number ending in 0 or 5 is divisible by 5: 1055.

2. 8. False

   Just look at the last digit of 861: is it 0, 2, 4, 6 or 8?

   Look at the last digit, 1: a number ending in 0, 2, 4, 6 or 8 is divisible by 2 and even; any other is odd.

3. 9. True

   Just look at the last digit of 2216: is it 0, 2, 4, 6 or 8?

   Look at the last digit, 6: a number ending in 0, 2, 4, 6 or 8 is divisible by 2 and even; any other is odd.

4. 10. False

   Add up the digits of 5521 and see whether the digit sum divides by 3.

   The digits add up to 13. If the digit sum is divisible by 3, so is the number; if not, nor is the number.

5. 11. B. 2680

   To divide by both 2 and 5, what must the last digit be? Check each choice's last digit.

   Divisible by both 2 and 5 means ending in 0 (divisible by 10): 2680.

6. 12. False

   Add up the digits of 508 and see whether the digit sum divides by 3.

   The digits add up to 13. If the digit sum is divisible by 3, so is the number; if not, nor is the number.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 9

   An odd number ends in an odd digit. Try the largest odd digit and work down, checking the digit sum is a multiple of 3.

   An odd number ends in 1, 3, 5, 7 or 9. Trying from 9 down, 4 + 5 + □ must be divisible by 3: □ = 9.

2. 14. 4 people

   Full rows of 5 means a number divisible by 5, ending in 0 or 5. Count on from 556.

   Full rows means divisible by 5: ending in 0 or 5. Counting on from 556 to the next one takes 4 more.

3. 15. 2 sweets

   Add up the digits of 691 and see how far it is to the next multiple of 3.

   The digits of 691 don't add to a multiple of 3. Counting on from 691, the first number divisible by 3 is 2 more.

4. 16. 6 numbers

   Numbers divisible by 10 end in 0. Find the first one from 363, then count one in every ten.

   Those divisible by 10 end in 0, one in every ten: counting them gives 6.

5. 17. 9

   An odd number ends in an odd digit. Try the largest odd digit and work down, checking the digit sum is a multiple of 3.

   An odd number ends in 1, 3, 5, 7 or 9. Trying from 9 down, 3 + 9 + □ must be divisible by 3: □ = 9.

6. 18. 4 people

   Full rows of 5 means a number divisible by 5, ending in 0 or 5. Count on from 791.

   Full rows means divisible by 5: ending in 0 or 5. Counting on from 791 to the next one takes 4 more.