[tex] xy=1000 [/tex]
1000|2
500|2
250|2
125|5
25|5
5|5
1
[tex] 1000=2^3\cdot5^3 \Leftrightarrow xy=2^3\cdot5^3 [/tex]
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 [tex] 2^3=8 [/tex] and the other [tex] 5^3=125 [/tex].
So, their sum is [tex] 8+125=133 [/tex]
