Divisible by 9: Digit Sum Trick, Examples, Chart, and Practice

What does divisible by 9 mean?

A number is divisible by 9 if you can divide it by 9 evenly.

Evenly means there is no remainder.

For example, 72 is divisible by 9 because 72 / 9 = 8 with no remainder.

But 74 is not divisible by 9 because 74 / 9 leaves 2 left over.

You can also think of it as making nine equal groups. If the groups are equal and nothing is left over, the number is divisible by 9.

Printable Divisible by 9 trick chart

Use this SumReflex chart to remember the digit-sum trick for divisibility by 9.

The same chart is also available in the Printable Number Reference Charts section with print and download buttons.

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The digit-sum trick

To check if a whole number is divisible by 9, add all the digits in the number.

If the digit sum is divisible by 9, the original number is divisible by 9.

If the digit sum is not divisible by 9, the original number is not divisible by 9.

For example, 729 has digit sum 7 + 2 + 9 = 18. Since 18 is divisible by 9, 729 is divisible by 9.

This is not a last-digit rule

The divisibility test for 9 is different from the test for 2, 5, or 10.

For 2, you can look at the last digit. For 9, the last digit alone does not decide the answer.

Example: 18 and 28 both end in 8. But 18 is divisible by 9, and 28 is not.

So when you test divisibility by 9, always add the digits.

Digit sums that show divisibility by 9

A digit sum works when it is a multiple of 9.

Common digit sums that work are 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, and 90.

If the digit sum is large, you can add its digits again. For example, 99 has digit sum 18, and 18 is divisible by 9.

Example: 9,999 has digit sum 9 + 9 + 9 + 9 = 36. Since 36 / 9 = 4, 9,999 is divisible by 9.

Why does the trick work?

The trick works because each place value is very close to a multiple of 9.

10 is 1 more than 9. 100 is 1 more than 99. 1,000 is 1 more than 999.

So each digit in a number leaves the same kind of remainder as that digit itself when you divide by 9.

That is why adding the digits tells you whether the original number divides evenly by 9.

Step-by-step method

Step 1: Add every digit in the number.

Step 2: Check the digit sum.

Step 3: If the digit sum is divisible by 9, the whole number is divisible by 9.

Step 4: If the digit sum is not divisible by 9, the whole number is not divisible by 9.

Example: 1,008 has digit sum 1 + 0 + 0 + 8 = 9. Since 9 is divisible by 9, 1,008 is divisible by 9.

Examples with solutions

Example 1: Is 729 divisible by 9? Add the digits: 7 + 2 + 9 = 18. Since 18 / 9 = 2, 729 is divisible by 9. 729 / 9 = 81.

Example 2: Is 738 divisible by 9? Add the digits: 7 + 3 + 8 = 18. Since 18 is divisible by 9, 738 is divisible by 9. 738 / 9 = 82.

Example 3: Is 742 divisible by 9? Add the digits: 7 + 4 + 2 = 13. Since 13 is not divisible by 9, 742 is not divisible by 9.

Example 4: Is 1,008 divisible by 9? Add the digits: 1 + 0 + 0 + 8 = 9. Since 9 is divisible by 9, 1,008 is divisible by 9. 1,008 / 9 = 112.

Example 5: Is 2,222 divisible by 9? Add the digits: 2 + 2 + 2 + 2 = 8. Since 8 is not divisible by 9, 2,222 is not divisible by 9.

Example 6: Is 9,999 divisible by 9? Add the digits: 9 + 9 + 9 + 9 = 36. Since 36 / 9 = 4, 9,999 is divisible by 9. 9,999 / 9 = 1,111.

Tougher examples

Example: Is 18,936 divisible by 9? Add the digits: 1 + 8 + 9 + 3 + 6 = 27. Since 27 / 9 = 3, 18,936 is divisible by 9. 18,936 / 9 = 2,104.

Example: Is 54,319 divisible by 9? Add the digits: 5 + 4 + 3 + 1 + 9 = 22. Since 22 is not divisible by 9, 54,319 is not divisible by 9.

Example: Is 100,008 divisible by 9? Add the digits: 1 + 0 + 0 + 0 + 0 + 8 = 9. Since 9 is divisible by 9, 100,008 is divisible by 9. 100,008 / 9 = 11,112.

Example: Is 3,006 divisible by 9? Add the digits: 3 + 0 + 0 + 6 = 9. Since 9 is divisible by 9, 3,006 is divisible by 9. 3,006 / 9 = 334.

Word problem examples

Example: A teacher has 729 stickers and wants to split them equally into 9 envelopes. Can she do it? The digit sum is 7 + 2 + 9 = 18, and 18 is divisible by 9. Yes. Each envelope gets 81 stickers.

Example: A game has 742 points to divide equally among 9 players. Can the points be shared with none left over? The digit sum is 13, and 13 is not divisible by 9. No.

Example: A factory packs 1,008 pencils into boxes of 9. Will there be any pencils left over? The digit sum is 9, so 1,008 is divisible by 9. No pencils are left over.

Common mistakes

Do not use only the last digit. Last-digit rules work for some numbers, but not for 9.

Do not stop just because the number is odd or even. Divisibility by 9 depends on the digit sum.

Do not confuse the rule for 3 with the rule for 9. Both use digit sums, but the sum must be divisible by 9 for the number to be divisible by 9.

Do not forget zeros. They do not change the sum, but they are still part of the number.

Quick practice

1. Is 81 divisible by 9? Answer: yes, because 8 + 1 = 9.

2. Is 217 divisible by 9? Answer: no, because 2 + 1 + 7 = 10.

3. Is 738 divisible by 9? Answer: yes, because 7 + 3 + 8 = 18.

4. Is 1,008 divisible by 9? Answer: yes, because 1 + 0 + 0 + 8 = 9.

5. Is 2,222 divisible by 9? Answer: no, because 2 + 2 + 2 + 2 = 8.

6. Is 4,509 divisible by 9? Answer: yes, because 4 + 5 + 0 + 9 = 18.

7. Is 9,999 divisible by 9? Answer: yes, because 9 + 9 + 9 + 9 = 36.

The big idea

Divisibility by 9 is a digit-sum rule.

Add all the digits in the number.

If the digit sum is divisible by 9, the number is divisible by 9.

If the digit sum is not divisible by 9, the number is not divisible by 9.