Greatest Common Factor of 120 and 9000
GCF(120, 9000) = 120, Greatest common factor of 120 and 9000 is 120. 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 9000. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 120 and 9000 by prime factorization method
We will first find the prime factorization of 120 and 9000.
Prime Factorization of 120 is 1, 2, 2, 2, 3, 5 and Prime Factorization of 9000 is 1, 2, 2, 2, 3, 3, 5, 5, 5.
- Factorize\( (120) = \) \(1\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (9000) = \) \(1\times 2\times 2\times 2\times 3\times 3\times 5\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 2, 3, 5) and multiply these numbers together.
\(GCF(120, 9000) = 1\times 2\times 2\times 2\times 3\times 5 = 120\).
Greatest Common Factor of 120 and 9000 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 9000 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000
As you can see, 120 is the greatest and common number that 120 and 9000 divides into.
So the greatest common factor 120 and 9000 is 120.
\(GCF(120, 9000) = 120\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
