What is the Divisibility Rule of 6?

The divisibility rule of 6 says that a number is divisible by 6 if it can be divided by both 2 and 3. First, check if the number is even (the last digit is 0, 2, 4, 6, or 8). Then, check if the sum of its digits is divisible by 3.

Complete Answer:

The divisibility rule of 6 helps us check if a number can be divided by 6 without actually dividing it. A number is divisible by 6 if it follows two rules:

1. It is divisible by 2: This means the number must be even. A number is even if its last digit is 0, 2, 4, 6, or 8.
2. It is divisible by 3: To check this, find the sum of the digits of the number. If the sum is divisible by 3, then the number is divisible by 3.

For example:
Take the number 54.

• It is even because the last digit is 4 (so divisible by 2).
• The sum of its digits is 5 + 4 = 9, which is divisible by 3.

Since 54 passes both rules, it is divisible by 6.

Additional Examples to test the Divisibility Rule of 6

Here are 5 examples to understand what is the divisibility rule of 6:

Example 1: 72

• Check if divisible by 2: As the last digit 2 is even, it is divisible by 2.
• Check if divisible by 3: Add each digit to get the sum of digits: 7 + 2 = 9. As the sum of digits in 9, it is divisible by 3.

Thus, 72 is divisible by 6.

Example 2: 45

Check if divisible by 2: As the last digit 5 is an odd number, it is not divisible by 2
Check if divisible by 3: The sum of digits: 4 + 5 = 9. Since the sum of each digit is 9, it is divisible by 3.

Thus, 45 is not divisible by 6 because it fails the first rule.

Example 3: 120

Check divisibility by 2: As the last digit 0 is an even number, it is divisible by 2.
Check divisibility by 3: Sum of digits: 1 + 2 + 0 = 3. Since the sum of digits is 3, it is divisible by 3.

Thus, 120 is divisible by 6.

Example 4: 81

Check if divisible by 2: As the last digit 1 is an odd number, it is not divisible by 2.
Check if divisible by 3: Calculate the Sum of digits: 8 + 1 = 9. Since the sum of digits is 9, it is divisible by 3.

Thus, 81 is not divisible by 6 because it fails the first rule that is it does not follow the divisibility by 2 rule.

Example 5: 96

Check if divisible by 2: As the last digit 6 is an even number, it is divisible by 2.

Check if divisible by 3: Add the digits: 9 + 6 = 15. As the sum of digits 15 is divisible by 3, the number follows the divisibility by 3 rule.

Thus, 96 is divisible by 6.

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