A number is divisible by 6,
if the last digit in the units place is 0 or even, and
the sum of the digits is divisible by 3
METHOD
Step 1. Check out the last digit. If the last digit in the units place is 0 or even, then proceed to Step 2.
Step 2. Add up the digits
Step 3. If the sum of the digits is divisible by 3, then the original number is divisible by 6.
Example 1. Consider the number 312
Step 1. The last digit is 2, which is even. Proceed with Step 2.
Step 2. 3 + 2 + 1 = 6
Step 3. 6 / 3 = 2 exactly
Since the sum of the digits is divisible by 3, so 312 is divisible by 6.
Check. 312 / 6 = 52 exactly
Example 2. Consider the number 8258
Step 1. The last digit is 2, which is even. Proceed with Step 2.
Step 2. 8 + 2 + 5 + 8 = 23
Step 3. 23 / 3 = 7 remain 2
Since the sum of digits is not divisible by 3, so 8258 is not divisible by 6.
Check. 8258 / 6 = 1376 remain 2
Example 3. Consider the number 21870
Step 1. The last digit is 2, which is 0. Proceed with Step 2.
Step 1, 2 + 1 + 8 + 7 + 0 = 18
Step 2. 18 / 3 = 6 exactly
Since the sum of the digits is divisible by 3, so 427 is divisible by 6.
Check. 21870 / 6 = 3645 exactly
Example 4. Consider the number 427
Step 1. The last digit is 7, which is odd
Odd number is not divisible by 6.
Check. 427 / 6 = 71 remain 1
| Number | Step 1 | Step 1 is 0 or even? | Step 2 | Step 3 | Step 3 Divisible by 3? | Number Divisible by 6? |
|---|---|---|---|---|---|---|
| 312 | 2 | Even | 3 + 2 + 1 = 6 | 6 / 3 = 2 exactly | Yes | Yes |
| 8258 | 8 | Even | 8 + 2 + 5 + 8 = 23 | 23 / 3 = 7 remain 2 | No | No |
| 21870 | 0 | Even | 2 + 1 + 8 + 7 + 0 = 18 | 18 / 3 = 6 exactly | Yes | Yes |
| 427 | 7 | Odd | No |
