Greatest Common Factor of 120 and 2300
GCF(120, 2300) = 20, Greatest common factor of 120 and 2300 is 20. 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 120 and 2300. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 120 and 2300 by prime factorization method
We will first find the prime factorization of 120 and 2300.
Prime Factorization of 120 is 1, 2, 2, 2, 3, 5 and Prime Factorization of 2300 is 1, 2, 2, 5, 5, 23.
- Factorize\( (120) = \) \(1\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (2300) = \) \(1\times 2\times 2\times 5\times 5\times 23\)
Now we need to find any which are common for each number (1, 2, 2, 5) and multiply these numbers together.
\(GCF(120, 2300) = 1\times 2\times 2\times 5 = 20\).
Greatest Common Factor of 120 and 2300 by matching factors method
List of positive integers factors of 120 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
List of positive integers factors of 2300 leaving a remainder zero is 1, 2, 4, 5, 10, 20, 23, 25, 46, 50, 92, 100, 115, 230, 460, 575, 1150, 2300
As you can see, 20 is the greatest and common number that 120 and 2300 divides into.
So the greatest common factor 120 and 2300 is 20.
\(GCF(120, 2300) = 20\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
