Q:

What is the GCF of 132 and 62?

Accepted Solution

A:
Solution: The GCF of 132 and 62 is 2 Methods How to find the GCF of 132 and 62 using Prime Factorization One way to find the GCF of 132 and 62 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 132? What are the Factors of 62? Here is the prime factorization of 132: 2 2 × 3 1 × 1 1 1 2^2 × 3^1 × 11^1 2 2 × 3 1 × 1 1 1 And this is the prime factorization of 62: 2 1 × 3 1 1 2^1 × 31^1 2 1 × 3 1 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 132 and 62 by multiplying all the matching prime factors to get a GCF of 132 and 62 as 4: Thus, the GCF of 132 and 62 is: 4 How to Find the GCF of 132 and 62 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 132 and 62 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, 132 and 62: Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 Factors of 62: 1, 2, 31, 62 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 132 and 62 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 12 and 142? What is the GCF of 58 and 71? What is the GCF of 7 and 108? What is the GCF of 66 and 135? What is the GCF of 57 and 3?