Q:

What is the GCF of 102 and 142?

Accepted Solution

A:
Solution: The GCF of 102 and 142 is 2 Methods How to find the GCF of 102 and 142 using Prime Factorization One way to find the GCF of 102 and 142 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 102? What are the Factors of 142? Here is the prime factorization of 102: 2 1 × 3 1 × 1 7 1 2^1 × 3^1 × 17^1 2 1 × 3 1 × 1 7 1 And this is the prime factorization of 142: 2 1 × 7 1 1 2^1 × 71^1 2 1 × 7 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 102 and 142 by multiplying all the matching prime factors to get a GCF of 102 and 142 as 4: Thus, the GCF of 102 and 142 is: 4 How to Find the GCF of 102 and 142 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 102 and 142 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, 102 and 142: Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102 Factors of 142: 1, 2, 71, 142 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 102 and 142 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 122 and 34? What is the GCF of 115 and 60? What is the GCF of 38 and 141? What is the GCF of 78 and 92? What is the GCF of 99 and 71?