Q:

What is the GCF of 66 and 111?

Accepted Solution

A:
Solution: The GCF of 66 and 111 is 3 Methods How to find the GCF of 66 and 111 using Prime Factorization One way to find the GCF of 66 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 66? What are the Factors of 111? Here is the prime factorization of 66: 2 1 × 3 1 × 1 1 1 2^1 × 3^1 × 11^1 2 1 × 3 1 × 1 1 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 66 and 111 by multiplying all the matching prime factors to get a GCF of 66 and 111 as 9: Thus, the GCF of 66 and 111 is: 9 How to Find the GCF of 66 and 111 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 66 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, 66 and 111: Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66 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, 3. Since 3 is the largest of these common factors, the GCF of 66 and 111 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 144 and 39? What is the GCF of 51 and 71? What is the GCF of 134 and 80? What is the GCF of 75 and 112? What is the GCF of 106 and 74?