How do you find the gcf of a fraction?

Answer 1

The general idea is to find a common factor between the numerator and the denominator, so that you can simplify the fraction.

One way is to find the prime factors for numerator and denominator, and look for common factors. This is appropriate for small numbers, but slow for larger numbers.

A much faster method for large numbers is Euclid's algorithm. For example, to find the gcf of 70 and 40, subtract 70 - 40. You get 30. The gcf of 70 and 40 is the same as the gcf of 40 and 30. Continue, until one number is a multiple of the other: gcf of 40 and 30 is the same as gcf of 30 and 10; since 30 is a multiple of 10, 10 is the gcf.