Question 24
The notation $n!$ (read “$n$ factorial”) is defined as the product of the first $n$ positive integers. (For example, $3! = 1 \cdot 2 \cdot 3 = 6.$) Define the *superfactorial* of a positive integer, denoted by $n^!,$ to be the product of the factorials of the first $n$ integers. (For example, $3^! = 1! \cdot 2! \cdot 3! = 12.$) How many factors of $7$ appear in the prime factorization of $51^!,$ the superfactorial of $51?$