Q:

What is the GCF of 34 and 51?

Accepted Solution

A:
Solution: The GCF of 34 and 51 is 17 Methods How to find the GCF of 34 and 51 using Prime Factorization One way to find the GCF of 34 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 34? What are the Factors of 51? 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 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 34 and 51 by multiplying all the matching prime factors to get a GCF of 34 and 51 as 289: Thus, the GCF of 34 and 51 is: 289 How to Find the GCF of 34 and 51 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 34 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, 34 and 51: Factors of 34: 1, 2, 17, 34 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, 17. Since 17 is the largest of these common factors, the GCF of 34 and 51 would be 17. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 113 and 80? What is the GCF of 144 and 56? What is the GCF of 101 and 89? What is the GCF of 126 and 137? What is the GCF of 63 and 5?