Question

If 1! +2! +3! +4! ……+100! is divided by 7, what is the remainder?

• A. 1
• B. 3
• C. 5
• D. 6

Answer 1

Answer:

C. 5

7!+8!+9!+⋯+100! is divisible by 7 and will have 0 remainder because 7 is a factor of this expression. So we need only to check that what will be the remainder when 1!+2!+3!+4!+5!+6! is divided by 7 1!+2!+3!+4!+5!+6!=1+2+6+24+120+720=873 873=124×7+5 Hence 5 will be the remainder