Q:

What is the GCF of 76 and 140?

Accepted Solution

A:
Solution: The GCF of 76 and 140 is 4 Methods How to find the GCF of 76 and 140 using Prime Factorization One way to find the GCF of 76 and 140 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 76? What are the Factors of 140? Here is the prime factorization of 76: 2 2 × 1 9 1 2^2 × 19^1 2 2 × 1 9 1 And this is the prime factorization of 140: 2 2 × 5 1 × 7 1 2^2 × 5^1 × 7^1 2 2 × 5 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 76 and 140 by multiplying all the matching prime factors to get a GCF of 76 and 140 as 4: Thus, the GCF of 76 and 140 is: 4 How to Find the GCF of 76 and 140 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 76 and 140 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, 76 and 140: Factors of 76: 1, 2, 4, 19, 38, 76 Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 76 and 140 would be 4. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 9 and 87? What is the GCF of 4 and 28? What is the GCF of 3 and 92? What is the GCF of 1 and 134? What is the GCF of 116 and 140?