common factor

**merenwen** · May 9th 2008, 06:39 AM

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

The answer is a3b2. Why??

Thanks for saving me!!

**TKHunny** · May 9th 2008, 08:18 AM

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

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

What's common between them?

**certainlycrystal** · June 11th 2013, 03:31 PM

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

**Plato** · June 11th 2013, 03:59 PM

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

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