# common factor

• May 9th 2008, 06:39 AM
merenwen
common factor
If a and b are prime numbers, what is the greatest common divisor of a4b2 and a3b3?

Thanks for saving me!!
• May 9th 2008, 08:18 AM
TKHunny
$a^{4}b^{2} = a*(a^{3}b^{2})$

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

What's common between them?
• June 11th 2013, 03:31 PM
certainlycrystal
Re: common factor
TKHunny, your answer makes sense to me.. but how did you arrive at it?
• June 11th 2013, 03:59 PM
Plato
Re: common factor
Quote:

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 $x=\min\{a,c\}~\&~y=\min\{c,d\}$