14. One of the following is the largest square that is a factor of $10!$. Which one?
Note that, $n!=1 \times 2 \times 3 \times \cdots \times(n-1) \times n$
A $(4!)^{2}$
B $(5!)^{2}$
$\mathrm{C}(6!)^{2}$
D $(7!)^{2}$
$\mathrm{E}(8!)^{2}$
Solution
C
CommENTARY
If you are familiar with the values of $n$ ! for small values of $n$, it is not difficult to spot the answer quite quickly, as in Method 1. If not, a more systematic method is to work out the prime factorization of 10 !, as in Method 2.