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## Divisibility Guidelines for 6, 8 and 12

In this post, we are going to learn about the guidelines behind knowing if a number is divisible by 6, 8, or 12. Divisibility guidelines for 6, 8 and 12. ##### Divisibility guidelines for 6:

To know if a number is divisible by 6, you have to first check if it is divisible by 3 and by 2. If it is divisible by 2 and by 3, then it is divisible by 6.

For example: Is 138 divisible by 6?

• First, we are going to check if it is divisible by 2: 138 ends in 8, which is an even number, therefore 138 is divisible by 2.
• Now, we are going to check if it is divisible by 3 by adding all the digits, 1 + 3 + 8 = 12. As 12 is divisible by 3, then 138 is also divisible by 3.
• Since 138 is divisible by both 3 and 2, 138 it is also divisible by 6.
##### Divisibility guidelines for 8:

To know if a number is divisible by 8, you have to first check if its last 3 digits are divisible by 8. If the last 3 digits are divisible by 8, then the whole number is also divisible by 8.

For example: Is 12856 divisible by 8?

• Let’s take the last 3 digits of 12856 and divide them by 8. 856/8 = 107
• Since we were left with no remainder, 856 is divisible by 8. Therefore, 12856 is indeed divisible by 8.
##### Divisibility guidelines for 12:

In order to know if a number is divisible by 12, you have to first check if it is divisible by 3 and 4. If it is divisible by both 3 and 4, then the number is divisible by 12.

For example: Is 168 divisible by 12?

• First, we are going to check if it is divisible by 3. To do that, we add its digits: 1 + 6 + 8 = 15. Since 15 is divisible by 3, 168 is also divisible by 3.
• Now we are going to check if it is divisible by 4. To do that, we divide its last 2 digits by 4. 68/4 = 17.
• Since there is no remainder, 68 is divisible by 4. Therefore, 168 is also divisible by 4.
• Therefore, since 168 is divisible by both 3 and 4, 168 is also divisible by 12.