Greatest Common Factor of 200 and 120
GCF(200, 120) = 40, Greatest common factor of 200 and 120 is 40. 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 200 and 120. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 200 and 120 by prime factorization method
We will first find the prime factorization of 200 and 120.
Prime Factorization of 200 is 1, 2, 2, 2, 5, 5 and Prime Factorization of 120 is 1, 2, 2, 2, 3, 5.
- Factorize\( (200) = \) \(1\times 2\times 2\times 2\times 5\times 5\)
- Factorize\( (120) = \) \(1\times 2\times 2\times 2\times 3\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 2, 5) and multiply these numbers together.
\(GCF(200, 120) = 1\times 2\times 2\times 2\times 5 = 40\).
Greatest Common Factor of 200 and 120 by matching factors method
List of positive integers factors of 200 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
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
As you can see, 40 is the greatest and common number that 200 and 120 divides into.
So the greatest common factor 200 and 120 is 40.
\(GCF(200, 120) = 40\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
