Q:

What is the GCF of 66 and 120?

Accepted Solution

A:
Solution: The GCF of 66 and 120 is 6 Methods How to find the GCF of 66 and 120 using Prime Factorization One way to find the GCF of 66 and 120 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 66? What are the Factors of 120? Here is the prime factorization of 66: 2 1 × 3 1 × 1 1 1 2^1 × 3^1 × 11^1 2 1 × 3 1 × 1 1 1 And this is the prime factorization of 120: 2 3 × 3 1 × 5 1 2^3 × 3^1 × 5^1 2 3 × 3 1 × 5 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 66 and 120 by multiplying all the matching prime factors to get a GCF of 66 and 120 as 36: Thus, the GCF of 66 and 120 is: 36 How to Find the GCF of 66 and 120 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 66 and 120 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, 66 and 120: Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66 Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 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 66 and 120 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 129? What is the GCF of 78 and 28? What is the GCF of 95 and 104? What is the GCF of 26 and 38? What is the GCF of 139 and 116?