SOLUTION: IF we 66^66÷64 what is remainder?

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Question 1185535: IF we 66^66÷64 what is remainder?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The number 66 contains one prime factor of 2 (66 = 2*3*11).

So the number 66^66 contains 66 prime factors of 2.

The divisor 64 is 2^6; that is, it contains 6 prime factors of 2.

So when 66^66 is divided by 64, there are plenty of factors of 2 in 66^66 to be canceled with the 6 factors of 2 in 64; the remainder is 0.

Formally....

66%5E66+=+%282%2A3%2A11%29%5E66