Q:

What is the GCF of 66 and 14?

Accepted Solution

A:
Solution: The GCF of 66 and 14 is 2 Methods How to find the GCF of 66 and 14 using Prime Factorization One way to find the GCF of 66 and 14 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 14? 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 14: 2 1 × 7 1 2^1 × 7^1 2 1 × 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 14 by multiplying all the matching prime factors to get a GCF of 66 and 14 as 4: Thus, the GCF of 66 and 14 is: 4 How to Find the GCF of 66 and 14 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 66 and 14 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 14: Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66 Factors of 14: 1, 2, 7, 14 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 66 and 14 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 71 and 93? What is the GCF of 12 and 34? What is the GCF of 117 and 14? What is the GCF of 143 and 39? What is the GCF of 24 and 92?