Q:

What is the GCF of 138 and 51?

Accepted Solution

A:
Solution: The GCF of 138 and 51 is 3 Methods How to find the GCF of 138 and 51 using Prime Factorization One way to find the GCF of 138 and 51 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 138? What are the Factors of 51? Here is the prime factorization of 138: 2 1 × 3 1 × 2 3 1 2^1 × 3^1 × 23^1 2 1 × 3 1 × 2 3 1 And this is the prime factorization of 51: 3 1 × 1 7 1 3^1 × 17^1 3 1 × 1 7 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 138 and 51 by multiplying all the matching prime factors to get a GCF of 138 and 51 as 9: Thus, the GCF of 138 and 51 is: 9 How to Find the GCF of 138 and 51 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 138 and 51 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, 138 and 51: Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138 Factors of 51: 1, 3, 17, 51 When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 138 and 51 would be 3. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 67 and 92? What is the GCF of 132 and 87? What is the GCF of 72 and 27? What is the GCF of 80 and 106? What is the GCF of 79 and 21?