Q:

What is the GCF of 98 and 148?

Accepted Solution

A:
Solution: The GCF of 98 and 148 is 2 Methods How to find the GCF of 98 and 148 using Prime Factorization One way to find the GCF of 98 and 148 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 98? What are the Factors of 148? Here is the prime factorization of 98: 2 1 × 7 2 2^1 × 7^2 2 1 × 7 2 And this is the prime factorization of 148: 2 2 × 3 7 1 2^2 × 37^1 2 2 × 3 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 98 and 148 by multiplying all the matching prime factors to get a GCF of 98 and 148 as 4: Thus, the GCF of 98 and 148 is: 4 How to Find the GCF of 98 and 148 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 98 and 148 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, 98 and 148: Factors of 98: 1, 2, 7, 14, 49, 98 Factors of 148: 1, 2, 4, 37, 74, 148 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 98 and 148 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 52 and 125? What is the GCF of 102 and 92? What is the GCF of 26 and 82? What is the GCF of 20 and 46? What is the GCF of 114 and 111?