Q:

What is the GCF of 108 and 58?

Accepted Solution

A:
Solution: The GCF of 108 and 58 is 2 Methods How to find the GCF of 108 and 58 using Prime Factorization One way to find the GCF of 108 and 58 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 108? What are the Factors of 58? Here is the prime factorization of 108: 2 2 × 3 3 2^2 × 3^3 2 2 × 3 3 And this is the prime factorization of 58: 2 1 × 2 9 1 2^1 × 29^1 2 1 × 2 9 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 108 and 58 by multiplying all the matching prime factors to get a GCF of 108 and 58 as 4: Thus, the GCF of 108 and 58 is: 4 How to Find the GCF of 108 and 58 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 108 and 58 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, 108 and 58: Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 Factors of 58: 1, 2, 29, 58 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 108 and 58 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 146 and 50? What is the GCF of 123 and 55? What is the GCF of 143 and 5? What is the GCF of 59 and 128? What is the GCF of 93 and 62?