Q:

What is the GCF of 58 and 108?

Accepted Solution

A:
Solution: The GCF of 58 and 108 is 2 Methods How to find the GCF of 58 and 108 using Prime Factorization One way to find the GCF of 58 and 108 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 58? What are the Factors of 108? Here is the prime factorization of 58: 2 1 × 2 9 1 2^1 × 29^1 2 1 × 2 9 1 And this is the prime factorization of 108: 2 2 × 3 3 2^2 × 3^3 2 2 × 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 58 and 108 by multiplying all the matching prime factors to get a GCF of 58 and 108 as 4: Thus, the GCF of 58 and 108 is: 4 How to Find the GCF of 58 and 108 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 58 and 108 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, 58 and 108: Factors of 58: 1, 2, 29, 58 Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 58 and 108 would be 2. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 24 and 141? What is the GCF of 145 and 10? What is the GCF of 63 and 28? What is the GCF of 7 and 65? What is the GCF of 48 and 135?