Q:

What is the GCF of 42 and 44?

Accepted Solution

A:
Solution: The GCF of 42 and 44 is 2 Methods How to find the GCF of 42 and 44 using Prime Factorization One way to find the GCF of 42 and 44 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 42? What are the Factors of 44? Here is the prime factorization of 42: 2 1 × 3 1 × 7 1 2^1 × 3^1 × 7^1 2 1 × 3 1 × 7 1 And this is the prime factorization of 44: 2 2 × 1 1 1 2^2 × 11^1 2 2 × 1 1 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 42 and 44 by multiplying all the matching prime factors to get a GCF of 42 and 44 as 4: Thus, the GCF of 42 and 44 is: 4 How to Find the GCF of 42 and 44 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 42 and 44 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, 42 and 44: Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Factors of 44: 1, 2, 4, 11, 22, 44 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 42 and 44 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 109 and 29? What is the GCF of 51 and 30? What is the GCF of 115 and 100? What is the GCF of 23 and 128? What is the GCF of 89 and 28?