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

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

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Answer 1 · 2016-06-11T23:19:43

$2$ 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 $64 + 40 >= 100$

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

1 Answer

Explanation:

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