Q:

What is the GCF of 38 and 114?

Accepted Solution

A:
Solution: The GCF of 38 and 114 is 38 Methods How to find the GCF of 38 and 114 using Prime Factorization One way to find the GCF of 38 and 114 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 38? What are the Factors of 114? Here is the prime factorization of 38: 2 1 × 1 9 1 2^1 × 19^1 2 1 × 1 9 1 And this is the prime factorization of 114: 2 1 × 3 1 × 1 9 1 2^1 × 3^1 × 19^1 2 1 × 3 1 × 1 9 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 38 and 114 by multiplying all the matching prime factors to get a GCF of 38 and 114 as 1444: Thus, the GCF of 38 and 114 is: 1444 How to Find the GCF of 38 and 114 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 38 and 114 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, 38 and 114: Factors of 38: 1, 2, 19, 38 Factors of 114: 1, 2, 3, 6, 19, 38, 57, 114 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 19, 38. Since 38 is the largest of these common factors, the GCF of 38 and 114 would be 38. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 15 and 133? What is the GCF of 66 and 97? What is the GCF of 42 and 31? What is the GCF of 51 and 34? What is the GCF of 144 and 23?