Q:

What is the GCF of 138 and 42?

Accepted Solution

A:
Solution: The GCF of 138 and 42 is 6 Methods How to find the GCF of 138 and 42 using Prime Factorization One way to find the GCF of 138 and 42 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 42? 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 42: 2 1 × 3 1 × 7 1 2^1 × 3^1 × 7^1 2 1 × 3 1 × 7 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 42 by multiplying all the matching prime factors to get a GCF of 138 and 42 as 36: Thus, the GCF of 138 and 42 is: 36 How to Find the GCF of 138 and 42 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 138 and 42 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 42: Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 138 and 42 would be 6. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 39 and 93? What is the GCF of 143 and 58? What is the GCF of 76 and 126? What is the GCF of 60 and 63? What is the GCF of 54 and 36?