Question

what iss the remainder of 12^50 when divided by 30?​

Answer 1

N=1!+2!+3!+4!+5!………+50!

Now 4!= 24

This shows 4! and all the factorial terms after that are surely divisible by 12.(For eg. 5!= 120…)

Therefore, N=1!+2!+3!+12(n)

N=1+2+6+12(n)

N=9+12(n)

Therefore the remainder when N is divided by 12 is 9.