Grade 4 number sense lesson
Divisible by 6: Two-Test Trick, Examples, Chart, and Practice
A whole number is divisible by 6 when it can be divided into six equal groups with no remainder. The fastest trick is to check divisibility by 2 and 3.
What does divisible by 6 mean?
A number is divisible by 6 if you can divide it by 6 evenly.
Evenly means there is no remainder.
For example, 42 is divisible by 6 because 42 / 6 = 7 with no remainder.
But 44 is not divisible by 6 because 44 / 6 leaves 2 left over.
You can also think of it as making six equal groups. If the groups are equal and nothing is left over, the number is divisible by 6.
Printable Divisible by 6 trick chart
Use this SumReflex chart to remember the two-test trick for divisibility by 6.
The same chart is also available in the Printable Number Reference Charts section with print and download buttons.
The two-test trick
To check if a whole number is divisible by 6, it must pass two tests.
Test 1: The number must be divisible by 2. That means the last digit must be 0, 2, 4, 6, or 8.
Test 2: The number must be divisible by 3. That means the sum of its digits must be divisible by 3.
If both tests are yes, the number is divisible by 6.
If even one test is no, the number is not divisible by 6.
How the last digit helps
The first part of the divisibility-by-6 trick is the same last digit trick used for divisibility by 2.
If the last digit is 0, 2, 4, 6, or 8, the number is even and passes the first test.
If the last digit is 1, 3, 5, 7, or 9, the number is odd and cannot be divisible by 6.
Example: 135 has digit sum 1 + 3 + 5 = 9, but it ends in 5. Since it is odd, 135 is not divisible by 6.
How the digit sum helps
The second part of the divisibility-by-6 trick is the digit-sum rule for divisibility by 3.
Add every digit in the number.
If the digit sum is 0, 3, 6, 9, 12, 15, 18, 21, and so on, the number passes the second test.
Example: 432 has digit sum 4 + 3 + 2 = 9. Since 9 is divisible by 3, 432 passes the divisibility-by-3 test.
Why does the trick work?
The trick works because 6 is made from 2 and 3.
A number divisible by 6 must be divisible by 2 and divisible by 3.
The number 2 checks whether a number is even.
The number 3 checks the digit sum pattern.
When both checks are true, the number can be divided evenly by 6.
Step-by-step method
Step 1: Check the last digit. If it is odd, the number is not divisible by 6.
Step 2: If the last digit is even, add all the digits.
Step 3: Check whether the digit sum is divisible by 3.
Step 4: If the number is even and the digit sum is divisible by 3, the number is divisible by 6.
Example: 1,002 ends in 2, so it is even. Its digit sum is 1 + 0 + 0 + 2 = 3. Since both checks are yes, 1,002 is divisible by 6.
Examples with solutions
Example 1: Is 126 divisible by 6? It ends in 6, so it is even. The digit sum is 1 + 2 + 6 = 9. Since 9 is divisible by 3, 126 is divisible by 6. 126 / 6 = 21.
Example 2: Is 128 divisible by 6? It ends in 8, so it is even. The digit sum is 1 + 2 + 8 = 11. Since 11 is not divisible by 3, 128 is not divisible by 6.
Example 3: Is 135 divisible by 6? The digit sum is 1 + 3 + 5 = 9, but the number ends in 5, so it is odd. 135 is not divisible by 6.
Example 4: Is 432 divisible by 6? It ends in 2, so it is even. The digit sum is 4 + 3 + 2 = 9. Both checks are yes, so 432 is divisible by 6. 432 / 6 = 72.
Example 5: Is 1,002 divisible by 6? It ends in 2, so it is even. The digit sum is 1 + 0 + 0 + 2 = 3. Both checks are yes, so 1,002 is divisible by 6. 1,002 / 6 = 167.
Example 6: Is 2,222 divisible by 6? It ends in 2, so it is even. The digit sum is 2 + 2 + 2 + 2 = 8. Since 8 is not divisible by 3, 2,222 is not divisible by 6.
Tougher examples
Example: Is 48,732 divisible by 6? It ends in 2, so it is even. The digit sum is 4 + 8 + 7 + 3 + 2 = 24. Since 24 is divisible by 3, 48,732 is divisible by 6.
Example: Is 91,426 divisible by 6? It ends in 6, so it is even. The digit sum is 9 + 1 + 4 + 2 + 6 = 22. Since 22 is not divisible by 3, 91,426 is not divisible by 6.
Example: Is 10,005 divisible by 6? The digit sum is 1 + 0 + 0 + 0 + 5 = 6, but the number ends in 5, so it is not divisible by 6.
Example: Is 3,006 divisible by 6? It ends in 6, so it is even. The digit sum is 3 + 0 + 0 + 6 = 9. Both checks are yes, so 3,006 is divisible by 6.
Word problem examples
Example: A teacher has 234 cards and wants to split them equally into 6 boxes. Can she do it? 234 ends in 4, so it is even. The digit sum is 2 + 3 + 4 = 9. Yes, each box gets 39 cards.
Example: There are 222 stickers. Can 6 students share them equally with none left over? 222 is even, and 2 + 2 + 2 = 6. Yes, each student gets 37 stickers.
Example: A game has 1,005 points to divide equally among 6 teams. The digit sum is 6, but the number ends in 5, so no. It is not divisible by 6.
Common mistakes
Do not check only the last digit. An even last digit only proves divisibility by 2, not divisibility by 6.
Do not check only the digit sum. A number can be divisible by 3 but still not divisible by 6 if it is odd.
Do not forget that both tests must be yes. One yes and one no means the number is not divisible by 6.
Do not confuse divisibility by 6 with skip counting by 6. Skip counting helps, but the two-test trick is faster for large numbers.
Quick practice
1. Is 42 divisible by 6? Answer: yes, because it is even and 4 + 2 = 6.
2. Is 75 divisible by 6? Answer: no, because it is odd.
3. Is 108 divisible by 6? Answer: yes, because it is even and 1 + 0 + 8 = 9.
4. Is 134 divisible by 6? Answer: no, because 1 + 3 + 4 = 8.
5. Is 216 divisible by 6? Answer: yes, because it is even and 2 + 1 + 6 = 9.
6. Is 1,005 divisible by 6? Answer: no, because it is odd.
7. Is 3,006 divisible by 6? Answer: yes, because it is even and 3 + 0 + 0 + 6 = 9.
The big idea
Divisibility by 6 is a two-test rule.
First, use the last digit to check divisibility by 2.
Then, use the digit sum to check divisibility by 3.
The number is divisible by 6 only when it passes both tests.