Q:

What is the GCF of 105 and 19?

Accepted Solution

A:
Solution: The GCF of 105 and 19 is 1MethodsHow to find the GCF of 105 and 19 using Prime FactorizationOne way to find the GCF of 105 and 19 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 105?What are the Factors of 19?Here is the prime factorization of 105:31Γ—51Γ—713^1 Γ— 5^1 Γ— 7^131Γ—51Γ—71And this is the prime factorization of 19:19119^1191When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 105 and 19 is 1.Thus, the GCF of 105 and 19 is: 1How to Find the GCF of 105 and 19 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 105 and 19 is to find and list all the factors of each number. Again, you can see how this is done by looking at the β€œFactors of” articles that are linked to above.Let’s take a look at the factors for each of these numbers, 105 and 19:Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105Factors of 19: 1, 19When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 105 and 19 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 129 and 106?What is the GCF of 93 and 4?What is the GCF of 73 and 84?What is the GCF of 63 and 43?What is the GCF of 75 and 81?