Elementary Mathematics Greatest Common Factor

Greatest Common Factor GCF

GFC – Listing the Factors Method The “Listing the Factors Method” is a comparison to find the largest number in a matching set of Factors between two unrelated numbers. Factors are a set of numbers that divide, or group, a given number evenly. Example: All of the possible factors for the number 24 are (1, 2, 3, 4, 6, 8, 12, 24). We can determine the factors through an exhaustive list of multiplications that equal 24. 1 x 24 = 24; 2 x 12 = 24; 3 x 8 = 24; 4 x 6 = 24; And… all of the possible factors for the number 36 are (1, 2, 3, 4, 6, 9, 12, 18, 36). We can determine the factors through an exhaustive list of multiplications that equal 36. 1 x 36 = 36; 2 x 18 = 36; 3 x 12 = 36; 4 x 9 = 36; 6 x 6 = 36; A matching set of Factors for the two numbers (24 & 36) equal (1, 2, 3, 4, 6, 12), the greatest of these matching Factors is the GCF between them. The GCF between 24 and 36 is 12.

The GCF Venn for common Factors of 24 and 36

GFC – Prime Factorization Method The “Prime Factorization Method” utilizes a factor tree to represent the product of a number in prime numbers only. We can then do a resulting comparison to determine the GCF between the two given numbers. Factor trees can begin with any two product factors of the comparison numbers. Example: We will use 48 and 72 as our two comparison numbers, the following trees can be constructed. 48 72 8 6 9 8 2 4 3 2 3 3 2 4 2 2 2 2 (2 x 2 x 2 x 3 x 2) (3 x 3 x 2 x 2 x 2) (2 x 2 x 2 x3) x (2) (3) x (3 x 2x 2 x 2) (24) x (2) (3) x (24) The GCF between 48 and 72 is 24.

The GCF Venn for common Prime Factors of 48 and 72