Q:

What is the GCF of 69 and 46?

Accepted Solution

A:
Solution: The GCF of 69 and 46 is 23 Methods How to find the GCF of 69 and 46 using Prime Factorization One way to find the GCF of 69 and 46 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 69? What are the Factors of 46? Here is the prime factorization of 69: 3 1 × 2 3 1 3^1 × 23^1 3 1 × 2 3 1 And this is the prime factorization of 46: 2 1 × 2 3 1 2^1 × 23^1 2 1 × 2 3 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 69 and 46 by multiplying all the matching prime factors to get a GCF of 69 and 46 as 529: Thus, the GCF of 69 and 46 is: 529 How to Find the GCF of 69 and 46 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 69 and 46 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, 69 and 46: Factors of 69: 1, 3, 23, 69 Factors of 46: 1, 2, 23, 46 When you compare the two lists of factors, you can see that the common factor(s) are 1, 23. Since 23 is the largest of these common factors, the GCF of 69 and 46 would be 23. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 135 and 26? What is the GCF of 63 and 86? What is the GCF of 34 and 67? What is the GCF of 32 and 117? What is the GCF of 143 and 107?