Perfect Square

What is the smallest positive integer $n$ such that $16!/n$ is a perfect square?
Source: NCTM Mathematics Teacher, December 2005

SOLUTION
$16!=16\cdot 15\cdot 14\cdots 3\cdot 2\cdot 1$
$16=2^4$
$15=3\cdot 5$
$14=2\cdot 7$
$13=1\cdot 13$
$12=2^2\cdot 3$
$11=1\cdot 11$
$10=2\cdot 5$
$9=3^2$
$8=2^3$
$7=1\cdot 7$
$6=2\cdot 3$
$5=1\cdot 5$
$4=2^2$
$3=1\cdot 3$
$2=1\cdot 2$
$16!=2^{15}\cdot 3^6\cdot 5^3\cdot 7^2\cdot 11\cdot 13$
$=(2^7)^2\cdot 2\cdot (3^3)^2\cdot 5^2\cdot 5\cdot 7^2\cdot 11\cdot 13$
$n$ will be smallest when we make the numerator as large a perfect square as it can be.
$n=2\cdot 5\cdot 11\cdot 13=1430$

Answer: $1430$