Q:

What is the GCF of 120 and 107?

Accepted Solution

A:
Solution: The GCF of 120 and 107 is 1 Methods How to find the GCF of 120 and 107 using Prime Factorization One way to find the GCF of 120 and 107 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 107? Here is the prime factorization of 120: 2 3 Γ— 3 1 Γ— 5 1 2^3 Γ— 3^1 Γ— 5^1 2 3 Γ— 3 1 Γ— 5 1 And this is the prime factorization of 107: 10 7 1 107^1 10 7 1 When 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 107 is 1. Thus, the GCF of 120 and 107 is: 1 How to Find the GCF of 120 and 107 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 120 and 107 is to find and list all the factors of each number. Again, you can see how this is done by looking at the β€œFactors of” articles that are linked to above. Let’s take a look at the factors for each of these numbers, 120 and 107: Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 Factors of 107: 1, 107 When 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 107 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 116 and 94? What is the GCF of 101 and 83? What is the GCF of 30 and 69? What is the GCF of 31 and 70? What is the GCF of 40 and 3?