Greatest Common Factor of 540 and 780
GCF(540, 780) = 60, Greatest common factor of 540 and 780 is 60. 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 780. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 540 and 780 by prime factorization method
We will first find the prime factorization of 540 and 780.
Prime Factorization of 540 is 1, 2, 2, 3, 3, 3, 5 and Prime Factorization of 780 is 1, 2, 2, 3, 5, 13.
- Factorize\( (540) = \) \(1\times 2\times 2\times 3\times 3\times 3\times 5\)
- Factorize\( (780) = \) \(1\times 2\times 2\times 3\times 5\times 13\)
Now we need to find any which are common for each number (1, 2, 2, 3, 5) and multiply these numbers together.
\(GCF(540, 780) = 1\times 2\times 2\times 3\times 5 = 60\).
Greatest Common Factor of 540 and 780 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 780 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
As you can see, 60 is the greatest and common number that 540 and 780 divides into.
So the greatest common factor 540 and 780 is 60.
\(GCF(540, 780) = 60\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
