Greatest Common Factor of 1200 and 1800
GCF(1200, 1800) = 600, Greatest common factor of 1200 and 1800 is 600. 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 1200 and 1800. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 1200 and 1800 by prime factorization method
We will first find the prime factorization of 1200 and 1800.
Prime Factorization of 1200 is 1, 2, 2, 2, 2, 3, 5, 5 and Prime Factorization of 1800 is 1, 2, 2, 2, 3, 3, 5, 5.
- Factorize\( (1200) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 5\times 5\)
- Factorize\( (1800) = \) \(1\times 2\times 2\times 2\times 3\times 3\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 2, 3, 5, 5) and multiply these numbers together.
\(GCF(1200, 1800) = 1\times 2\times 2\times 2\times 3\times 5\times 5 = 600\).
Greatest Common Factor of 1200 and 1800 by matching factors method
List of positive integers factors of 1200 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200
List of positive integers factors of 1800 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, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800
As you can see, 600 is the greatest and common number that 1200 and 1800 divides into.
So the greatest common factor 1200 and 1800 is 600.
\(GCF(1200, 1800) = 600\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
