Question

If `345,987,091,543,0?4` is divisible by `8`, then what can the missing digit be?

Answer 1

`2` or `6`

Explanation:

First note that `1000 = 2^3*5^3` is divisible by `8=2^3`, so we can ignore the initial `345,987,091,543` part of the number when assessing divisibility by `8`.

We can ignore the leading `0` of the remaining `3` digits too.

So we are looking for `2` digit numbers ending in `4` and divisible by `8`.

`24 = 8 * 3` works

The next solution is `24+40 = 64`, since `40` is the least common multiple of `10` and `8`.

There are no more solutions since `24 - 40 < 0` and `64 + 40 >= 100`