# Reducing fractions.

1. Apr 30, 2008

### Holocene

Is there any way to derive the greatest common divisor from the prime factorizations of the numerator and denominator?

For instance:

$$\displaystyle{\frac{48}{150} = \frac{ 2 * 2 * 2 * 2 * 3}{2 * 3 * 5 * 5}}$$

The GCD = 6 in this example, but is there any way to determine that from the prime factorizations alone?

2. Apr 30, 2008

### CRGreathouse

Yes, that's the easiest (if not fastest) way. Just choose pairs of identical prime factors until none are left that match, then multiply the primes together.