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Math Tutor Solution: The GCF of 105 and 34 is 1
Methods
How to find the GCF of 105 and 34 using Prime Factorization
One way to find the GCF of 105 and 34 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
Here is the prime factorization of 105:
And this is the prime factorization of 34:
When 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 34 is 1.
Thus, the GCF of 105 and 34 is: 1
How to Find the GCF of 105 and 34 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 34 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 34:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 34: 1, 2, 17, 34
When 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 34 is 1.
Math Tutor Suggests: Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems walkthrough from math tutors:
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