Q:

What is the GCF of 117 and 42?

Accepted Solution

A:
Solution: The GCF of 117 and 42 is 3 Methods How to find the GCF of 117 and 42 using Prime Factorization One way to find the GCF of 117 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 117? What are the Factors of 42? Here is the prime factorization of 117: 3 2 × 1 3 1 3^2 × 13^1 3 2 × 1 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 117 and 42 by multiplying all the matching prime factors to get a GCF of 117 and 42 as 9: Thus, the GCF of 117 and 42 is: 9 How to Find the GCF of 117 and 42 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 117 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, 117 and 42: Factors of 117: 1, 3, 9, 13, 39, 117 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, 3. Since 3 is the largest of these common factors, the GCF of 117 and 42 would be 3. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 50 and 18? What is the GCF of 129 and 62? What is the GCF of 86 and 11? What is the GCF of 56 and 127? What is the GCF of 40 and 101?