Q:

What is the GCF of 126 and 84?

Accepted Solution

A:
Solution: The GCF of 126 and 84 is 42 Methods How to find the GCF of 126 and 84 using Prime Factorization One way to find the GCF of 126 and 84 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 126? What are the Factors of 84? Here is the prime factorization of 126: 2 1 × 3 2 × 7 1 2^1 × 3^2 × 7^1 2 1 × 3 2 × 7 1 And this is the prime factorization of 84: 2 2 × 3 1 × 7 1 2^2 × 3^1 × 7^1 2 2 × 3 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 126 and 84 by multiplying all the matching prime factors to get a GCF of 126 and 84 as 1764: Thus, the GCF of 126 and 84 is: 1764 How to Find the GCF of 126 and 84 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 126 and 84 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, 126 and 84: Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6, 7, 14, 21, 42. Since 42 is the largest of these common factors, the GCF of 126 and 84 would be 42. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 49 and 66? What is the GCF of 20 and 4? What is the GCF of 63 and 61? What is the GCF of 9 and 115? What is the GCF of 97 and 107?