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The product of two natural numbers is 1000. None of them is divisible by 10. Find their sum.

User Istrel
by
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1 Answer

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xy=1000


1000|2

500|2

250|2

125|5

25|5

5|5

1



1000=2^3\cdot5^3 \Leftrightarrow xy=2^3\cdot5^3


If those two numbers are not divisble by 10, then neither of them can have both 2 and 5 as prime factors, since 2*5=10. Then one of the numbers must be
2^3=8 and the other
5^3=125.


So, their sum is
8+125=133



User Pajm
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