(Q). If S is the sum of factorial of all the prime numbers less than 150. Then what will be the last three digit of S.
Solution:- Since the last three digits of factorials greater than or equal to 15! are ‘000’. Hence we need not to consider factorial greater than or equal to 15 because summation of these will not contribute anything in last three digits.
Hence we need to find the sum of all prime numbers less than 15!.
2! ⟶ 2
3! ⟶ 6
5! ⟶ 120
7! ⟶ 5040
11! ⟶ 39916800
13! ⟶ 6007020800