Greatest Common Factor of 300 and 1350
GCF(300, 1350) = 150, Greatest common factor of 300 and 1350 is 150. 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 300 and 1350. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 300 and 1350 by prime factorization method
We will first find the prime factorization of 300 and 1350.
Prime Factorization of 300 is 1, 2, 2, 3, 5, 5 and Prime Factorization of 1350 is 1, 2, 3, 3, 3, 5, 5.
- Factorize\( (300) = \) \(1\times 2\times 2\times 3\times 5\times 5\)
- Factorize\( (1350) = \) \(1\times 2\times 3\times 3\times 3\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 3, 5, 5) and multiply these numbers together.
\(GCF(300, 1350) = 1\times 2\times 3\times 5\times 5 = 150\).
Greatest Common Factor of 300 and 1350 by matching factors method
List of positive integers factors of 300 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
List of positive integers factors of 1350 leaving a remainder zero is 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350
As you can see, 150 is the greatest and common number that 300 and 1350 divides into.
So the greatest common factor 300 and 1350 is 150.
\(GCF(300, 1350) = 150\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
