Q:

What is the GCF of 120 and 137?

Accepted Solution

A:
Solution: The GCF of 120 and 137 is 1MethodsHow to find the GCF of 120 and 137 using Prime FactorizationOne way to find the GCF of 120 and 137 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 120?What are the Factors of 137?Here is the prime factorization of 120:23×31×512^3 × 3^1 × 5^123×31×51And this is the prime factorization of 137:1371137^11371When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 120 and 137 is 1.Thus, the GCF of 120 and 137 is: 1How to Find the GCF of 120 and 137 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 120 and 137 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, 120 and 137:Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120Factors of 137: 1, 137When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 120 and 137 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 54 and 4?What is the GCF of 117 and 76?What is the GCF of 115 and 75?What is the GCF of 108 and 121?What is the GCF of 109 and 15?