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.

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About mvtrinh

Retired high school math teacher.
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