Answer:
252, 522, 222, and 552
Explanation:
For a number to be divisible by 6, it needs to be divisible by both 2 and 3. For a number to be divisible by 2, it needs to end in an even number, and the only even number we can use is 2.
So far our number is _ _ 2.
For a number to be divisible by three, its digits have to add up to a multiple of three. As of now we need to fill in the hundreds and tens place, and there are 4 combinations to check: 2, 5; 5, 2; 2, 2; and 5, 5.
Case #1: 2, 5
We are checking to see if the number 252 is divisible by six.
2 + 5 + 2 = 9
Since the numbers add up to a multiple of 3, 252 is divisible by 6.
Case #2: 5, 2
We are checking to see if the number 522 is divisible by six.
5 + 2 + 2 = 9
Since the numbers add up to a multiple of 3, 522 is divisible by 6.
Case #3: 2, 2
We are checking to see if the number 222 is divisible by six.
2 + 2 + 2 = 6
Since the numbers add up to a multiple of 3, 222 is divisible by 6.
Case #4: 5, 5
We are checking to see if the number 552 is divisible by six.
5 + 5 + 2 = 12
Since the numbers add up to a multiple of 3, 552 is divisible by 6.