Divisibility Rule For 6 With Examples

Divisibility Rule for 6

A number is divisible by 6 if it meets two conditions:

1. It is divisible by 2.
2. It is divisible by 3.

Detailed Explanation

1. Divisibility by 2:

• A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

1. Divisibility by 3:

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

Steps to Check Divisibility by 6

1. Check if the last digit is even (for divisibility by 2).
2. Calculate the sum of the digits and check if that sum is divisible by 3.

If both conditions are satisfied, the number is divisible by 6.

Visual Representation

Even Last Digits for Divisibility by 2:

• 0, 2, 4, 6, 8

Sum of Digits for Divisibility by 3:

• Example: For the number 123, the sum is ( 1 + 2 + 3 = 6), which is divisible by 3.

Examples

1. Example 1: 12

• Check for 2: Last digit is 2 (even) → Yes.
• Check for 3: ( 1 + 2 = 3 ) (divisible by 3) → Yes.
• Conclusion: 12 is divisible by 6.

1. Example 2: 18

• Check for 2: Last digit is 8 (even) → Yes.
• Check for 3: ( 1 + 8 = 9 ) (divisible by 3) → Yes.
• Conclusion: 18 is divisible by 6.

1. Example 3: 25

• Check for 2: Last digit is 5 (odd) → No.
• Conclusion: 25 is not divisible by 6.

1. Example 4: 24

• Check for 2: Last digit is 4 (even) → Yes.
• Check for 3: ( 2 + 4 = 6 ) (divisible by 3) → Yes.
• Conclusion: 24 is divisible by 6.

1. Example 5: 30

• Check for 2: Last digit is 0 (even) → Yes.
• Check for 3: ( 3 + 0 = 3 ) (divisible by 3) → Yes.
• Conclusion: 30 is divisible by 6.

Summary

To determine if a number is divisible by 6, check if:

• The last digit is even (for divisibility by 2).
• The sum of the digits is divisible by 3.

If both conditions are met, the number is divisible by 6.