Q:

What is the GCF of 84 and 35?

Accepted Solution

A:
Solution: The GCF of 84 and 35 is 7 Methods How to find the GCF of 84 and 35 using Prime Factorization One way to find the GCF of 84 and 35 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 84? What are the Factors of 35? Here is the prime factorization of 84: 2 2 × 3 1 × 7 1 2^2 × 3^1 × 7^1 2 2 × 3 1 × 7 1 And this is the prime factorization of 35: 5 1 × 7 1 5^1 × 7^1 5 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 84 and 35 by multiplying all the matching prime factors to get a GCF of 84 and 35 as 49: Thus, the GCF of 84 and 35 is: 49 How to Find the GCF of 84 and 35 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 84 and 35 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, 84 and 35: Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Factors of 35: 1, 5, 7, 35 When you compare the two lists of factors, you can see that the common factor(s) are 1, 7. Since 7 is the largest of these common factors, the GCF of 84 and 35 would be 7. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 12 and 118? What is the GCF of 3 and 41? What is the GCF of 127 and 130? What is the GCF of 11 and 147? What is the GCF of 116 and 138?