Zeroes VII

Factorial \( n \) or \( n! \) is defined as below: $$ n! = 1 \times 2 \times 3 \times \dots \times n $$ For example, \( 7! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 = 5040 \). Now, if we prime factorize a factorial, we will be able to find the frequency of each prime in it. For example, \( 7! = 5040 = 2^4 \times 3^2 \times 5 \times 7 \). So there are exactly four \( 2 \)'s, two \