Q:

What is the GCF of 138 and 69?

Accepted Solution

A:
Solution: The GCF of 138 and 69 is 69 Methods How to find the GCF of 138 and 69 using Prime Factorization One way to find the GCF of 138 and 69 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 69? 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 69: 3 1 × 2 3 1 3^1 × 23^1 3 1 × 2 3 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 69 by multiplying all the matching prime factors to get a GCF of 138 and 69 as 4761: Thus, the GCF of 138 and 69 is: 4761 How to Find the GCF of 138 and 69 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 138 and 69 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 69: Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138 Factors of 69: 1, 3, 23, 69 When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 23, 69. Since 69 is the largest of these common factors, the GCF of 138 and 69 would be 69. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 49 and 100? What is the GCF of 95 and 116? What is the GCF of 135 and 65? What is the GCF of 17 and 146? What is the GCF of 148 and 85?