Question

Using no other digits except 2 and 5 write down, if possible, a three-digit multiple of 6

Answer 1

225

Explanation:

Some other numbers that would work are:

255, 525, 555

Answer 2

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.