Question

Let A be a digit. If the 7-digit number 353808A is divisible by 2, 3, 4, 5, 6, 8, and 9, then what is A?

Answer 1

0

Explanation:

For the number to be divisible by 5, its units digit must be a 5 or a 0. In addition, for the number to be divisible by 2, the units digit must be even. Thus, A must be
`$\boxed{0}$`.

Note that when A=0, we also have the following:

* The sum of the digits of the number is 27, so the number is divisible by 3 and 9. * The number formed by the last two digits is 80, which is a multiple of 4, so the number is divisible by 4.

* The number is divisible by 2 and by 3, so it is divisible by 6.

* The number formed by the last three digits is 080, which is a multiple of 8, so the number is divisible by 8.

Hope this helped! :)

Answer 2

0

Explanation:

The only two numbers that would make the whole expression divisible by 8 are 0 and 8. Since the number also has to be divisible by 5, though, the last digit must be a 0 or a 5. Therefore, A=0. Hope this helps!