Q:

What is the GCF of 38 and 88?

Accepted Solution

A:
Solution: The GCF of 38 and 88 is 2 Methods How to find the GCF of 38 and 88 using Prime Factorization One way to find the GCF of 38 and 88 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 88? 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 88: 2 3 × 1 1 1 2^3 × 11^1 2 3 × 1 1 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 88 by multiplying all the matching prime factors to get a GCF of 38 and 88 as 4: Thus, the GCF of 38 and 88 is: 4 How to Find the GCF of 38 and 88 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 38 and 88 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 88: Factors of 38: 1, 2, 19, 38 Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88 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 38 and 88 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 148 and 141? What is the GCF of 32 and 144? What is the GCF of 25 and 51? What is the GCF of 59 and 42? What is the GCF of 61 and 129?