Factorial, factorial, factorial

Algebra Level 2

\[ 1\times2\times3\times\cdots \times6 = (1\times2\times3)\times(1\times2\times3\times4\times5) \]

Extending the above to a larger number, we find that there exists an integer \(N\, (>6)\) such that \[ 1\times2\times3\times\cdots \times N = (1\times2\times3\times \cdots \times A)\times(1\times2\times3\times\cdots\times B), \] where \(A\) and \(B\) are both integers larger than 1.