Q:

What is the GCF of 22 and 46?

Accepted Solution

A:
Solution: The GCF of 22 and 46 is 2 Methods How to find the GCF of 22 and 46 using Prime Factorization One way to find the GCF of 22 and 46 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 22? What are the Factors of 46? Here is the prime factorization of 22: 2 1 × 1 1 1 2^1 × 11^1 2 1 × 1 1 1 And this is the prime factorization of 46: 2 1 × 2 3 1 2^1 × 23^1 2 1 × 2 3 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 22 and 46 by multiplying all the matching prime factors to get a GCF of 22 and 46 as 4: Thus, the GCF of 22 and 46 is: 4 How to Find the GCF of 22 and 46 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 22 and 46 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, 22 and 46: Factors of 22: 1, 2, 11, 22 Factors of 46: 1, 2, 23, 46 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 22 and 46 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 115 and 47? What is the GCF of 5 and 6? What is the GCF of 137 and 13? What is the GCF of 61 and 132? What is the GCF of 148 and 143?