Q:

What is the GCF of 126 and 50?

Accepted Solution

A:
Solution: The GCF of 126 and 50 is 2 Methods How to find the GCF of 126 and 50 using Prime Factorization One way to find the GCF of 126 and 50 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 50? 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 50: 2 1 × 5 2 2^1 × 5^2 2 1 × 5 2 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 50 by multiplying all the matching prime factors to get a GCF of 126 and 50 as 4: Thus, the GCF of 126 and 50 is: 4 How to Find the GCF of 126 and 50 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 126 and 50 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 50: Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 Factors of 50: 1, 2, 5, 10, 25, 50 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 126 and 50 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 39 and 76? What is the GCF of 94 and 142? What is the GCF of 18 and 49? What is the GCF of 16 and 92? What is the GCF of 27 and 50?