Factorial

Number Theory Level 2

$n!$ is the factorial of $n$ , where $n!=1\cdot 2\cdot 3\cdot ...\cdot \left( n-1 \right) \cdot n$ . For example $4!=1\cdot 2\cdot 3\cdot 4=24$ .

If $n!={ 2 }^{ 15 }\cdot { 3 }^{ 6 }\cdot { 5 }^{ 3 }\cdot { 7 }^{ 2 }\cdot 11\cdot 13$ what is the value of $n$ ?