Q:

What is the GCF of 114 and 74?

Accepted Solution

A:
Solution: The GCF of 114 and 74 is 2 Methods How to find the GCF of 114 and 74 using Prime Factorization One way to find the GCF of 114 and 74 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 114? What are the Factors of 74? Here is the prime factorization of 114: 2 1 × 3 1 × 1 9 1 2^1 × 3^1 × 19^1 2 1 × 3 1 × 1 9 1 And this is the prime factorization of 74: 2 1 × 3 7 1 2^1 × 37^1 2 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 114 and 74 by multiplying all the matching prime factors to get a GCF of 114 and 74 as 4: Thus, the GCF of 114 and 74 is: 4 How to Find the GCF of 114 and 74 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 114 and 74 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, 114 and 74: Factors of 114: 1, 2, 3, 6, 19, 38, 57, 114 Factors of 74: 1, 2, 37, 74 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 114 and 74 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 72 and 86? What is the GCF of 90 and 15? What is the GCF of 33 and 19? What is the GCF of 56 and 44? What is the GCF of 105 and 35?