Q:

What is the GCF of 84 and 2?

Accepted Solution

A:
Solution: The GCF of 84 and 2 is 2 Methods How to find the GCF of 84 and 2 using Prime Factorization One way to find the GCF of 84 and 2 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 2? 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 2: 2 1 2^1 2 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 2 by multiplying all the matching prime factors to get a GCF of 84 and 2 as 4: Thus, the GCF of 84 and 2 is: 4 How to Find the GCF of 84 and 2 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 84 and 2 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 2: Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Factors of 2: 1, 2 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 84 and 2 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 44 and 101? What is the GCF of 100 and 34? What is the GCF of 33 and 126? What is the GCF of 43 and 117? What is the GCF of 5 and 120?