## M and N

$M$ and $N$ are positive integers and neither of [them] are divisible by $10$. If the product of $M$ and $N$ equals $200000$, find the absolute value of the difference of $M$ and $N$.
Source: mathcontest.olemiss.edu 10/8/2012

SOLUTION
$M\times N=200000$
$= 2^6\times 5^5$
Since $M$ and $N$ are not divisible by $10=2\times 5$, neither of them contains a mix of 2 and 5.
$M=2^6=64$
$N=5^5=3125$
$|M-N|=|64-3125|$
$=|-3061|$
$=3061$

Answer: $3061$.