Q:

What is the GCF of 120 and 27?

Accepted Solution

A:
Solution: The GCF of 120 and 27 is 3 Methods How to find the GCF of 120 and 27 using Prime Factorization One way to find the GCF of 120 and 27 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 27? Here is the prime factorization of 120: 2 3 × 3 1 × 5 1 2^3 × 3^1 × 5^1 2 3 × 3 1 × 5 1 And this is the prime factorization of 27: 3 3 3^3 3 3 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 120 and 27 by multiplying all the matching prime factors to get a GCF of 120 and 27 as 9: Thus, the GCF of 120 and 27 is: 9 How to Find the GCF of 120 and 27 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 120 and 27 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 27: Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 Factors of 27: 1, 3, 9, 27 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 120 and 27 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 114 and 65? What is the GCF of 57 and 115? What is the GCF of 113 and 103? What is the GCF of 13 and 20? What is the GCF of 141 and 147?