Is 3081 divisible by 9? Its digit sum is □, and the digit sum leaves □ when divided by 9. Fill in each blank

12, 3. 3 + 0 + 8 + 1 = 12, and 12 ÷ 9 leaves 3. Only a remainder of 0 means divisible by 9.

6264 is divisible by 4. True or false?

True. Only the last two digits matter: 64 ÷ 4 leaves 0. The whole number is divisible by 4 only when they make a multiple of 4 (remainder 0).

The four-digit number □822 is divisible by 9. What digit goes in □?

6. The known digits add up to 8 + 2 + 2 = 12. With □ the sum must be a multiple of 9, so it is 18 and □ is 6. A four-digit number can't start with 0.

Working with numbers · Ages 12–13

Divisibility by 4, 6, 8 and 9

4: last two digits. 8: last three. 9: digit sum. 6: both 2 and 3.

How to do it

Method

4: last two digits. 8: last three. 9: digit sum. 6: both 2 and 3

7236: 36 = 4 × 9, 7 + 2 + 3 + 6 = 18

Another way

Just divide

7236 ÷ 4 = 1809

In full

You can tell without dividing. For 4, check whether the last two digits make a multiple of 4; for 8, the last three digits a multiple of 8; for 9, whether the digit sum is a multiple of 9; for 6, it must divide by both 2 and 3 (even, with a digit sum that is a multiple of 3). Take 7236: its last two digits, 36 = 4 × 9, so 4 divides it; its digits add to 7 + 2 + 3 + 6 = 18, so 9 does too. Or simply divide: 7236 ÷ 4 = 1809.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
Is 3081 divisible by 9? Its digit sum is , and the digit sum leaves when divided by 9.
Fill in each blank
Show the answer and working
Answer: 12, 3
3 + 0 + 8 + 1 = 12, and 12 ÷ 9 leaves 3. Only a remainder of 0 means divisible by 9.
Example 2
6264 is divisible by 4.
True or false?
Show the answer and working
Answer: True
Only the last two digits matter: 64 ÷ 4 leaves 0. The whole number is divisible by 4 only when they make a multiple of 4 (remainder 0).
Example 3
The four-digit number 822 is divisible by 9. What digit goes in ?
Show the answer and working
Answer: 6
The known digits add up to 8 + 2 + 2 = 12. With □ the sum must be a multiple of 9, so it is 18 and □ is 6. A four-digit number can't start with 0.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Is 7565 divisible by 9? Its digit sum is , and the digit sum leaves when divided by 9.
Fill in each blank
Answer:
2.7787 is divisible by 9.
True or false?
Answer:
3.7156 is divisible by 4.
True or false?
Answer:
4.The four-digit number 779 is divisible by 6. What is the smallest digit that can go in ?
Answer:
5.The four-digit number 853 is divisible by 9. What is the smallest digit that can go in ?
Answer:

All the answers

1. 23, 5
2. False
3. True
4. 4
5. 2

Free worksheet: Divisibility by 4, 6, 8 and 9Working out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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