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## Main Question or Discussion Point

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?

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?