Q:

What is the GCF of 148 and 111?

Accepted Solution

A:
Solution: The GCF of 148 and 111 is 37 Methods How to find the GCF of 148 and 111 using Prime Factorization One way to find the GCF of 148 and 111 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 148? What are the Factors of 111? Here is the prime factorization of 148: 2 2 × 3 7 1 2^2 × 37^1 2 2 × 3 7 1 And this is the prime factorization of 111: 3 1 × 3 7 1 3^1 × 37^1 3 1 × 3 7 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 148 and 111 by multiplying all the matching prime factors to get a GCF of 148 and 111 as 1369: Thus, the GCF of 148 and 111 is: 1369 How to Find the GCF of 148 and 111 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 148 and 111 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, 148 and 111: Factors of 148: 1, 2, 4, 37, 74, 148 Factors of 111: 1, 3, 37, 111 When you compare the two lists of factors, you can see that the common factor(s) are 1, 37. Since 37 is the largest of these common factors, the GCF of 148 and 111 would be 37. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 127 and 133? What is the GCF of 62 and 10? What is the GCF of 136 and 13? What is the GCF of 27 and 70? What is the GCF of 106 and 53?