Factorial

n!n! is the factorial of nn, where n!=123...(n1)nn!=1\cdot 2\cdot 3\cdot ...\cdot \left( n-1 \right) \cdot n. For example 4!=1234=244!=1\cdot 2\cdot 3\cdot 4=24.

If n!=2153653721113n!={ 2 }^{ 15 }\cdot { 3 }^{ 6 }\cdot { 5 }^{ 3 }\cdot { 7 }^{ 2 }\cdot 11\cdot 13 what is the value of nn?

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