Q:

What is the GCF of 141 and 105?

Accepted Solution

A:
Solution: The GCF of 141 and 105 is 3 Methods How to find the GCF of 141 and 105 using Prime Factorization One way to find the GCF of 141 and 105 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 141? What are the Factors of 105? Here is the prime factorization of 141: 3 1 × 4 7 1 3^1 × 47^1 3 1 × 4 7 1 And this is the prime factorization of 105: 3 1 × 5 1 × 7 1 3^1 × 5^1 × 7^1 3 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 141 and 105 by multiplying all the matching prime factors to get a GCF of 141 and 105 as 9: Thus, the GCF of 141 and 105 is: 9 How to Find the GCF of 141 and 105 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 141 and 105 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, 141 and 105: Factors of 141: 1, 3, 47, 141 Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105 When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 141 and 105 would be 3. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 15 and 68? What is the GCF of 106 and 18? What is the GCF of 120 and 114? What is the GCF of 41 and 10? What is the GCF of 88 and 44?