Prime Factors of 20 Factorial

Example of Factorial
The prime decomposition of $20!$ is given as:


 * $20! = 2^{18} \times 3^8 \times 5^4 \times 7^2 \times 11 \times 13 \times 17 \times 19$

Proof
For each prime factor $p$ of $20!$, let $a_p$ be the integer such that:
 * $p^{a_p} \mathrel \backslash 20!$
 * $p^{a_p + 1} \nmid 20!$

Taking the prime factors in turn:

Similarly:


 * $a_{11} = 1$
 * $a_{13} = 1$
 * $a_{17} = 1$
 * $a_{19} = 1$

Hence the result.