If the sum of 1! + 2! + 3! + 4! + ... + 49! + 50! is divided by 15, what is the remainder?

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1. Every number above 14! will have zero remainder, since 15 is one of its factors. So, ask the same question about 1! + 2! + 3! + ...14!

All terms greater than 5! have both 3 and 5 as factors, so ask the same question about 1! + 2! + 3! + 4!

That sum is 33. Dividing that by 15 gives 3 with a remainder of 3.

The remainer of the full sum up to 50!divided by 15 will also be 3.

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posted by drwls

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