Divisibility Rules for 3, 6, and 9

# Divisibility Rules for 3, 6, and 9

• Divisibility by 3
• Divisibility by 6
• Divisibility by 9
• Summary
• Did You Know?
• What’s Next?

In the previous segment, we learnt the rules for divisibility by 5 and 10. In this segment, we will look at divisibility by 3, 6, and 9.

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## Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

For example,

• Consider 25722.

The sum of its digits is 2 + 5 + 7 + 2 + 2 = 18.

18 is divisible by 3. Hence, 25722 is divisible by 3.

• Consider 889992.

The sum of the digits is 8 + 8 + 9 + 9 + 9 + 2 = 45

Now, 45 can be further reduced to 4 + 5 = 9.

9 is divisible by 3. Hence, 889992 is divisible by 3.

## Divisibility by 6

A number is divisible by 6 if the number is even and it is divisible by 3.

For example,

• Consider 479623.

The last digit here is 3 and 3 is not divisible by 2. So, it is not an even number. Since the first condition is not fulfilled, there is no need to check if the second condition is satisfied or not.

Hence, 479623 is not divisible by 6.

• Consider 190116.

The last digit of this number is 6 which is divisible by 2. So, it is an even number. The sum of the digits for the given number is 1 + 9 + 0 + 1 + 1 + 6 = 18.

18 is divisible by 3. Hence, the number is divisible by 3.

As 190116 is an even number and is divisible by 3, it is divisible by 6.

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