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Reducing fractions.

  1. Apr 30, 2008 #1
    Is there any way to derive the greatest common divisor from the prime factorizations of the numerator and denominator?

    For instance:

    [tex]\displaystyle{\frac{48}{150} = \frac{ 2 * 2 * 2 * 2 * 3}{2 * 3 * 5 * 5}}[/tex]

    The GCD = 6 in this example, but is there any way to determine that from the prime factorizations alone?
  2. jcsd
  3. Apr 30, 2008 #2


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    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.
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