Divisibility Test: Is 564 Divisible by 3?

To determine if the number 564 is divisible by 3, we apply the divisibility rule for 3:

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

Let's calculate the sum of the digits of 564:

$5 + 6 + 4 = 15$

Next, we check if 15 is divisible by 3. Since 15 can be divided by 3 without a remainder, it is divisible by 3:

$15 \div 3 = 5$

Therefore, based on the divisibility rule, 564 is divisible by 3.

Thus, the correct answer is Yes.