Q:

What is the GCF of 45 and 132?

Accepted Solution

A:
Solution: The GCF of 45 and 132 is 3 Methods How to find the GCF of 45 and 132 using Prime Factorization One way to find the GCF of 45 and 132 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 45? What are the Factors of 132? Here is the prime factorization of 45: 3 2 × 5 1 3^2 × 5^1 3 2 × 5 1 And this 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 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 45 and 132 by multiplying all the matching prime factors to get a GCF of 45 and 132 as 9: Thus, the GCF of 45 and 132 is: 9 How to Find the GCF of 45 and 132 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 45 and 132 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, 45 and 132: Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 45 and 132 would be 3. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 29 and 27? What is the GCF of 62 and 12? What is the GCF of 8 and 96? What is the GCF of 50 and 70? What is the GCF of 37 and 134?