Greatest Common Factor of 60 and 2109
GCF(60, 2109) = 3, Greatest common factor of 60 and 2109 is 3. 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 2109. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 60 and 2109 by prime factorization method
We will first find the prime factorization of 60 and 2109.
Prime Factorization of 60 is 1, 2, 2, 3, 5 and Prime Factorization of 2109 is 1, 3, 19, 37.
- Factorize\( (60) = \) \(1\times 2\times 2\times 3\times 5\)
- Factorize\( (2109) = \) \(1\times 3\times 19\times 37\)
Now we need to find any which are common for each number (1, 3) and multiply these numbers together.
\(GCF(60, 2109) = 1\times 3 = 3\).
Greatest Common Factor of 60 and 2109 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 2109 leaving a remainder zero is 1, 3, 19, 37, 57, 111, 703, 2109
As you can see, 3 is the greatest and common number that 60 and 2109 divides into.
So the greatest common factor 60 and 2109 is 3.
\(GCF(60, 2109) = 3\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
