Q:

What is the GCF of 42 and 54?

Accepted Solution

A:
Solution: The GCF of 42 and 54 is 6 Methods How to find the GCF of 42 and 54 using Prime Factorization One way to find the GCF of 42 and 54 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 54? 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 54: 2 1 × 3 3 2^1 × 3^3 2 1 × 3 3 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 54 by multiplying all the matching prime factors to get a GCF of 42 and 54 as 36: Thus, the GCF of 42 and 54 is: 36 How to Find the GCF of 42 and 54 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 42 and 54 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 54: Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 42 and 54 would be 6. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 104 and 115? What is the GCF of 100 and 92? What is the GCF of 50 and 135? What is the GCF of 98 and 75? What is the GCF of 9 and 11?