To learn how to find the greatest common factor of two numbers, students learn that they must first identify all the possible factors of each of the two numbers. Once these pairs of factors have been identified, the greatest common factor is the largest number that appears in both sets of pairs of factors.
Students have previously learned to simplify a fraction (reduce a fraction) by rewriting it as an equivalent fraction with a smaller denominator.
In this lesson, students learn to use the greatest common factor of two numbers to simplify a fraction (reduce a fraction) to its simplest terms, or lowest terms. When a fraction is written in simplest terms, it means that the fraction has been rewritten as an equivalent fraction with the smallest denominator possible.
First, they learn to find the greatest common factor of the numerator and denominator of a given fraction. Next, they divide both the numerator and the denominator by the greatest common factor. The resulting fraction is the original fraction rewritten in lowest terms, or simplest terms.