How Do You Know if a Number is Divisible by 6?

A number is divisible by 6 if it's divisible by both 2 and 3.

The divisibility rule for 6 combines the rules for divisibility by 2 and 3. Let's break it down:

Divisibility by 2: A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8). This means the number is even.
Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.

Therefore, to check if a number is divisible by 6:

Check for divisibility by 2: Is the last digit even?
Check for divisibility by 3: Add up all the digits. Is the sum divisible by 3?

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

Examples

Let's look at a few examples:

12: The last digit is 2 (even), and 1 + 2 = 3 (divisible by 3). Therefore, 12 is divisible by 6.
24: The last digit is 4 (even), and 2 + 4 = 6 (divisible by 3). Therefore, 24 is divisible by 6.
35: The last digit is 5 (odd), so it's not divisible by 2, and thus not divisible by 6.
21: The last digit is 1 (odd), so it's not divisible by 2, and thus not divisible by 6. Even though 2 + 1 = 3 (divisible by 3), it fails the first condition.
36: The last digit is 6 (even), and 3 + 6 = 9 (divisible by 3). Therefore, 36 is divisible by 6.

As noted by multiple sources like Byju's (https://byjus.com/maths/divisibility-rules/) and Cuemath (https://www.cuemath.com/numbers/divisibility-rule-of-6/), a number must satisfy both conditions to be divisible by 6.