The greatest common factor (GCF) is the greatest number that is a factor of two or more numbers. The first step for finding a GCF is to list the factors of the numbers. Then we can find which one is the greatest.
Given Numbers
Factors
GCF
24
1, 2, 4, 6, 8, 12, 24
12
72
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
12
132
1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
12
The GCF of 24, 72, and 132 is 12.
Alternative Solution
Finding the GCF Using Prime Factorization
We can also find the GCF using prime factorization. To do so, we will follow 3 steps.
Write the prime factorization for the given numbers.
Mark the common prime factors.
Multiply the marked factors. The product is the GCF.
Let's begin by finding the prime factorizations! The prime factorization of a composite number is the number written as a product of its prime factors. We will use factor pairs and a factor tree to find the prime factorization of 24, 72, and 132. The factor tree is complete when only prime factors appear in the product. Let's start with 24!
We found that the prime factorization of 24 is 2 * 2 * 2 * 3. Let's repeat the process with 72.
The prime factorization of the composite number 72 is 2 * 2 * 2 * 3 *3. Let's continue with 132.
The prime factorization of 132 is 2 * 2* 3 * 11.
24 &= 2 * 2 * 2 * 3
72 &= 2 * 2 * 2 * 3 *3
132 & = 2 * 2* 3 * 11
The common prime factor of 24, 72, and 132 are 2, 2, and 3.
24 &= 2 * 2 * 2 * 3
72 &= 2 * 2 * 2 * 3 *3
132 & = 2 * 2* 3 * 11
The product of the marked factors is the GCF of the given numbers.
GCF: 2 * 2 * 3 = 12
This method led us to the same answer, so we know the answer is reasonable.
