Puzzle on Number System - What is the remainder left after dividing 1! + 2! + 3! + … + 100! By 7?

Question:  What is the remainder left after dividing 1! + 2! + 3! + … + 100! By 7?

Answer:    After Dividing we Get 5 as remainder

Solution: 

7! onward all terms are divisible by 7 as 7 is one of the factor. So there is no remainder left for those terms i.e. remainder left after dividing 7! + 8! + 9! + ... + 100! is 0.

The only part to be consider is

= 1! + 2! + 3! + 4! + 5! + 6!

= 1 + 2 + 6 + 24 + 120 + 720

= 873

The remainder left after dividing 873 by 7 is 5

Hence, the remainder is 5.