Greatest Common Factor of 60 and 105
GCF(60, 105) = 15, Greatest common factor of 60 and 105 is 15. Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the numbers can be divided. There are two different methods to calculate Greatest Common Factor of 60 and 105. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 60 and 105 by prime factorization method
We will first find the prime factorization of 60 and 105.
Prime Factorization of 60 is 1, 2, 2, 3, 5 and Prime Factorization of 105 is 1, 3, 5, 7.
- Factorize\( (60) = \) \(1\times 2\times 2\times 3\times 5\)
- Factorize\( (105) = \) \(1\times 3\times 5\times 7\)
Now we need to find any which are common for each number (1, 3, 5) and multiply these numbers together.
\(GCF(60, 105) = 1\times 3\times 5 = 15\).
Greatest Common Factor of 60 and 105 by matching factors method
List of positive integers factors of 60 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
List of positive integers factors of 105 leaving a remainder zero is 1, 3, 5, 7, 15, 21, 35, 105
As you can see, 15 is the greatest and common number that 60 and 105 divides into.
So the greatest common factor 60 and 105 is 15.
\(GCF(60, 105) = 15\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
