How to Find x + y When xy = 1,000 Without Using 10 as a Factor?

[mustang]

If x and y are whole numbers that don't have10 as a factor, and if xy = 1,000, find x + y.

 

[turin]

Make a list of prime factors of 1000. Distribute this into two sub-lists. Make sure that neither sub-list contains a 2 and 5 in the same sub-list. Hint, there are 6 prime factors, only two distinct, and only one way to divy them up according to these rules.

 

[mustang]

The list

I need more help.!

 

[recon]

This is what turin means

1000 = 5*5*5*2*2*2

To distribute this into sublists looks like this:

2         2*2*5*5*5
2*2      2*5*5*5

But we can't have both 2 and 5 in either sublists (that would give us a multiple of 10).

So the only way to resolve this is to have all the two's in one sublist and the three 5's in the other sublists, so we have: 2*2*2= 8 and 5*5*5 = 125.

x = 8, y=125