posted by .

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

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.

## Similar Questions

1. ### Math - repost for Anonymous

Can someone show me the steps to these questions (I will provide the correct answers)?
2. ### math

what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and …
3. ### math

what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and …
4. ### Math

Find the least positive integer that leaves the remainder 3 when divided by 7, remainder 4 when divided by 9, and remainder 8 when divided by 11. Using the Chinese Remainder Theorem.
5. ### Math

When 17 is divided by k,where k is a positive integer less than 17,,the remainder is 3.What is the remainder when the sum of the possible values of k is divided by 17?
6. ### Math

How many integers bewteen 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4?
7. ### Math

How many integers between 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4?
8. ### math

When a is divided by 7,the remainder is 4.When b is divided by 3,the remainder is 2.If 0<a<24 and 2<b<8, which of the following could have a remainder of 0 when divided by 8?
9. ### math

1.) when the expression 4x^2-3x-8 is divided by x-a, the remainder is 2. find the value of a. 2.) the polynomial 3x^3+mx^2+nx+5 leaves a remainder of 128 when divided by x-3 and a remainder of 4 when divided by x+1. calculate the remainder …