the product of two integers is 2^7*3^3*5^5*7^3 then the sum of the n\two numbers may be divisible by?

Question

a)16
b)9
c)25
d)49

Answer 1

c) 25

You need enough prime factors to put half in both.

In other words, to have the sum be divisible by 16 you would need 2^4 in one and 2^4 in the other, but you only have 2^7.

Similarly for 9, you would need 3^2 and 3^2, but you only have 3^3.

And for 49, you would need 7^2 and 7^2, but you only have 7^3.

However, for 25, you can have 5^2 and 5^2 because you have 5^5.

Note: The question says they *may* be divisible by... it is still possible to make it so they aren't divisible by 25, but there is at least one way that they may be divisible by 25.