Q:

What is the GCF of 138 and 122?

Accepted Solution

A:
Solution: The GCF of 138 and 122 is 2 Methods How to find the GCF of 138 and 122 using Prime Factorization One way to find the GCF of 138 and 122 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here: What are the Factors of 138? What are the Factors of 122? Here is the prime factorization of 138: 2 1 × 3 1 × 2 3 1 2^1 × 3^1 × 23^1 2 1 × 3 1 × 2 3 1 And this is the prime factorization of 122: 2 1 × 6 1 1 2^1 × 61^1 2 1 × 6 1 1 When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 138 and 122 by multiplying all the matching prime factors to get a GCF of 138 and 122 as 4: Thus, the GCF of 138 and 122 is: 4 How to Find the GCF of 138 and 122 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 138 and 122 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above. Let’s take a look at the factors for each of these numbers, 138 and 122: Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138 Factors of 122: 1, 2, 61, 122 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 138 and 122 would be 2. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 4 and 58? What is the GCF of 91 and 21? What is the GCF of 125 and 15? What is the GCF of 27 and 135? What is the GCF of 34 and 52?