Q:

What is the GCF of 70 and 126?

Accepted Solution

A:
Solution: The GCF of 70 and 126 is 14 Methods How to find the GCF of 70 and 126 using Prime Factorization One way to find the GCF of 70 and 126 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 70? What are the Factors of 126? Here is the prime factorization of 70: 2 1 × 5 1 × 7 1 2^1 × 5^1 × 7^1 2 1 × 5 1 × 7 1 And this is the prime factorization of 126: 2 1 × 3 2 × 7 1 2^1 × 3^2 × 7^1 2 1 × 3 2 × 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 70 and 126 by multiplying all the matching prime factors to get a GCF of 70 and 126 as 196: Thus, the GCF of 70 and 126 is: 196 How to Find the GCF of 70 and 126 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 70 and 126 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, 70 and 126: Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 7, 14. Since 14 is the largest of these common factors, the GCF of 70 and 126 would be 14. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 36 and 47? What is the GCF of 66 and 146? What is the GCF of 53 and 131? What is the GCF of 118 and 20? What is the GCF of 125 and 11?