Q:

What is the GCF of 74 and 134?

Accepted Solution

A:
Solution: The GCF of 74 and 134 is 2 Methods How to find the GCF of 74 and 134 using Prime Factorization One way to find the GCF of 74 and 134 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 74? What are the Factors of 134? Here is the prime factorization of 74: 2 1 × 3 7 1 2^1 × 37^1 2 1 × 3 7 1 And this is the prime factorization of 134: 2 1 × 6 7 1 2^1 × 67^1 2 1 × 6 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 74 and 134 by multiplying all the matching prime factors to get a GCF of 74 and 134 as 4: Thus, the GCF of 74 and 134 is: 4 How to Find the GCF of 74 and 134 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 74 and 134 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, 74 and 134: Factors of 74: 1, 2, 37, 74 Factors of 134: 1, 2, 67, 134 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 74 and 134 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 91 and 76? What is the GCF of 88 and 148? What is the GCF of 57 and 111? What is the GCF of 49 and 47? What is the GCF of 71 and 105?