The remainder when the sum 1! + 2! + 3! + ……. + 50! is divided by 10 is

To solve this problem, we need to understand the properties of factorials and how they relate to the division remainder.

1. Calculate the factorial for each number from 1 to 10. The results are: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800.

2. Notice that starting from 5!, the last digit of each factorial is 0. This is because the factorial operation involves multiplying by all integers up to the number, so once you multiply by 10 (which is part of the multiplication for all factorials starting from 5!), the result will end in 0.

3. Therefore, when you add up all the factorials from 1! to 50!, the last digit (which determines the remainder when divided by 10) is only affected by the factorials from 1! to 4!.

4. Add up the last digit of the factorials from 1! to 4!: 1 + 2 + 6 + 4 = 13.

5. The remainder when 13 is divided by 10 is 3.

So, the remainder when the sum 1! + 2! + 3! + ……. + 50! is divided by 10 is 3.