Q:

What is the GCF of 42 and 106?

Accepted Solution

A:
Solution: The GCF of 42 and 106 is 2 Methods How to find the GCF of 42 and 106 using Prime Factorization One way to find the GCF of 42 and 106 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 106? 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 106: 2 1 × 5 3 1 2^1 × 53^1 2 1 × 5 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 42 and 106 by multiplying all the matching prime factors to get a GCF of 42 and 106 as 4: Thus, the GCF of 42 and 106 is: 4 How to Find the GCF of 42 and 106 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 42 and 106 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 106: Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Factors of 106: 1, 2, 53, 106 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 106 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 19 and 98? What is the GCF of 65 and 45? What is the GCF of 27 and 10? What is the GCF of 111 and 55? What is the GCF of 15 and 25?