Q:

What is the GCF of 105 and 49?

Accepted Solution

A:
Solution: The GCF of 105 and 49 is 7MethodsHow to find the GCF of 105 and 49 using Prime FactorizationOne way to find the GCF of 105 and 49 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 49?Here is the prime factorization of 105:31×51×713^1 × 5^1 × 7^131×51×71And this is the prime factorization of 49:727^272When 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 105 and 49 by multiplying all the matching prime factors to get a GCF of 105 and 49 as 49:Thus, the GCF of 105 and 49 is: 49How to Find the GCF of 105 and 49 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 105 and 49 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, 105 and 49:Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105Factors of 49: 1, 7, 49When 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 105 and 49 would be 7.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 116 and 53?What is the GCF of 130 and 139?What is the GCF of 64 and 94?What is the GCF of 126 and 79?What is the GCF of 147 and 4?