Q:

What is the GCF of 126 and 16?

Accepted Solution

A:
Solution: The GCF of 126 and 16 is 2 Methods How to find the GCF of 126 and 16 using Prime Factorization One way to find the GCF of 126 and 16 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 16? 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 16: 2 4 2^4 2 4 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 16 by multiplying all the matching prime factors to get a GCF of 126 and 16 as 4: Thus, the GCF of 126 and 16 is: 4 How to Find the GCF of 126 and 16 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 126 and 16 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 16: Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 Factors of 16: 1, 2, 4, 8, 16 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 16 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 29 and 85? What is the GCF of 79 and 112? What is the GCF of 32 and 2? What is the GCF of 80 and 16? What is the GCF of 36 and 55?