Question

How do you prove 11111…1 (81 ones) is divisible by 81?

Answer 1

Answer:

If we split up the number n having 81 ones into 9 blocks of 9 ones each, like this:

n=111111111|111111111|111111111|111111111|111111111|111111111|111111111|111111111|111111111

we notice that

n=111111111×10000000100000001000000010000000100000001000000010000000100000001.

Both of the above numbers have exactly 9 ones, and no other nonzero digits. Hence, they are both divisible by 9, because the sum of their digits is divisible by 9. Consequently, n is divisible by 9×9=81, as required.

Step-by-step explanation:

Answer 2

Answer:

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