Prime factors

[lazyfox]

You feedback appreciated.

if v and w are positive integers and every prime factor of w is also a prime factor of v, is v/w an integer?

I understand that if v were to have every factor that w had then v/w is an integer.

[tohellandback]

it depends upon the powers of those prime factors
2=2
4=2^2
2/4 is not an integer though both have the same prime factors.

for v/w to be an integer, the prime factors must have higher powers (or at least same as w)in v
ex:1000=2^3*5^3
100=2^2*5^2
here 1000/100 is an integer because powers of 2 and 5 are bigger in 1000

[lazyfox]

Thanks tohellandback for the clarification. I guess when I see this statement "all prime factors of a number" then its essentially means that "all distinct prime factors of a number".