Question

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

Answer 1

`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`