Question

The remainder obtained when 1! + 2! + 3! + . . . + 77! is divided by 7 is:

• A. 5
• B. 4
• C. can't be determined

Answer 1

The correct option is A 5

Please remember that all the factorial numbers greater than or equal to n are divisible by n. Hence 7!, 8!, 9!, 10!, . . . etc are divisible by 7. So we have to check only
1! + 2! + 3! + 4! + 5! + 6!.
Hence 1! + 3! + 4! + 5! + 6!
=1 + 2 + 6 + 24 + 120 + 720 = 873
Thus 873 leaves a remainder of 5 when divided by 7. Therefore 1! + 2! + 3! + 4! + 5! + ... + 77 ! leaves remainder 5.