Q:

What is the GCF of 106 and 38?

Accepted Solution

A:
Solution: The GCF of 106 and 38 is 2MethodsHow to find the GCF of 106 and 38 using Prime FactorizationOne way to find the GCF of 106 and 38 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 106?What are the Factors of 38?Here is the prime factorization of 106:21×5312^1 × 53^121×531And this is the prime factorization of 38:21×1912^1 × 19^121×191When 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 106 and 38 by multiplying all the matching prime factors to get a GCF of 106 and 38 as 4:Thus, the GCF of 106 and 38 is: 4How to Find the GCF of 106 and 38 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 106 and 38 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, 106 and 38:Factors of 106: 1, 2, 53, 106Factors of 38: 1, 2, 19, 38When 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 106 and 38 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 125 and 43?What is the GCF of 61 and 26?What is the GCF of 101 and 82?What is the GCF of 79 and 72?What is the GCF of 24 and 108?