Q:

What is the GCF of 34 and 124?

Accepted Solution

A:
Solution: The GCF of 34 and 124 is 2 Methods How to find the GCF of 34 and 124 using Prime Factorization One way to find the GCF of 34 and 124 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 34? What are the Factors of 124? Here is the prime factorization of 34: 2 1 × 1 7 1 2^1 × 17^1 2 1 × 1 7 1 And this is the prime factorization of 124: 2 2 × 3 1 1 2^2 × 31^1 2 2 × 3 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 34 and 124 by multiplying all the matching prime factors to get a GCF of 34 and 124 as 4: Thus, the GCF of 34 and 124 is: 4 How to Find the GCF of 34 and 124 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 34 and 124 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, 34 and 124: Factors of 34: 1, 2, 17, 34 Factors of 124: 1, 2, 4, 31, 62, 124 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 34 and 124 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 64 and 19? What is the GCF of 10 and 131? What is the GCF of 113 and 102? What is the GCF of 72 and 143? What is the GCF of 8 and 81?