Q:

What is the GCF of 52 and 60?

Accepted Solution

A:
Solution: The GCF of 52 and 60 is 4 Methods How to find the GCF of 52 and 60 using Prime Factorization One way to find the GCF of 52 and 60 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 52? What are the Factors of 60? Here is the prime factorization of 52: 2 2 × 1 3 1 2^2 × 13^1 2 2 × 1 3 1 And this is the prime factorization of 60: 2 2 × 3 1 × 5 1 2^2 × 3^1 × 5^1 2 2 × 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 52 and 60 by multiplying all the matching prime factors to get a GCF of 52 and 60 as 4: Thus, the GCF of 52 and 60 is: 4 How to Find the GCF of 52 and 60 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 52 and 60 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, 52 and 60: Factors of 52: 1, 2, 4, 13, 26, 52 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 52 and 60 would be 4. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 51 and 93? What is the GCF of 71 and 149? What is the GCF of 31 and 144? What is the GCF of 32 and 41? What is the GCF of 101 and 85?