Greatest Common Factor of 540 and 1725
GCF(540, 1725) = 15, Greatest common factor of 540 and 1725 is 15. 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 540 and 1725. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 540 and 1725 by prime factorization method
We will first find the prime factorization of 540 and 1725.
Prime Factorization of 540 is 1, 2, 2, 3, 3, 3, 5 and Prime Factorization of 1725 is 1, 3, 5, 5, 23.
- Factorize\( (540) = \) \(1\times 2\times 2\times 3\times 3\times 3\times 5\)
- Factorize\( (1725) = \) \(1\times 3\times 5\times 5\times 23\)
Now we need to find any which are common for each number (1, 3, 5) and multiply these numbers together.
\(GCF(540, 1725) = 1\times 3\times 5 = 15\).
Greatest Common Factor of 540 and 1725 by matching factors method
List of positive integers factors of 540 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
List of positive integers factors of 1725 leaving a remainder zero is 1, 3, 5, 15, 23, 25, 69, 75, 115, 345, 575, 1725
As you can see, 15 is the greatest and common number that 540 and 1725 divides into.
So the greatest common factor 540 and 1725 is 15.
\(GCF(540, 1725) = 15\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
