Q:

What is the GCF of 72 and 52?

Accepted Solution

A:
Solution: The GCF of 72 and 52 is 4 Methods How to find the GCF of 72 and 52 using Prime Factorization One way to find the GCF of 72 and 52 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 72? What are the Factors of 52? Here is the prime factorization of 72: 2 3 × 3 2 2^3 × 3^2 2 3 × 3 2 And this is the prime factorization of 52: 2 2 × 1 3 1 2^2 × 13^1 2 2 × 1 3 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 72 and 52 by multiplying all the matching prime factors to get a GCF of 72 and 52 as 4: Thus, the GCF of 72 and 52 is: 4 How to Find the GCF of 72 and 52 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 72 and 52 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, 72 and 52: Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Factors of 52: 1, 2, 4, 13, 26, 52 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 72 and 52 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 141 and 31? What is the GCF of 150 and 127? What is the GCF of 46 and 140? What is the GCF of 118 and 43? What is the GCF of 145 and 13?