# Math Help - common factor

1. ## common factor

If a and b are prime numbers, what is the greatest common divisor of a4b2 and a3b3?

Thanks for saving me!!

2. $a^{4}b^{2} = a*(a^{3}b^{2})$

$a^{3}b^{3} = (a^{3}b^{2})*b$

What's common between them?

3. ## Re: common factor

TKHunny, your answer makes sense to me.. but how did you arrive at it?

4. ## Re: common factor

Originally Posted by certainlycrystal
TKHunny, your answer makes sense to me.. but how did you arrive at it?
Suppose that $p~\&~q$ are prime and each of $a,~b,~c,~\&~d$ is a non-negative integer then:

$\text{GCD}(p^aq^b,p^cq^d)=p^xq^y$ where $x=\min\{a,c\}~\&~y=\min\{c,d\}$