Divisibility Test: Is 684 Divisible by 6?

To determine if the number 684 is divisible by 6, we will apply the relevant divisibility rules:

• Divisibility by 2: A number is divisible by 2 if its last digit is even. The last digit of 684 is 4, which is even. Therefore, 684 is divisible by 2.
• Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 684 is $6 + 8 + 4 = 18$. Since 18 is divisible by 3 (because $18 \div 3 = 6$), 684 is divisible by 3.

Since 684 is divisible by both 2 and 3, it is divisible by 6.

Therefore, the solution to the problem is Yes.