Greatest Common Factor of 540 and 9024
GCF(540, 9024) = 12, Greatest common factor of 540 and 9024 is 12. 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 9024. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 540 and 9024 by prime factorization method
We will first find the prime factorization of 540 and 9024.
Prime Factorization of 540 is 1, 2, 2, 3, 3, 3, 5 and Prime Factorization of 9024 is 1, 2, 2, 2, 2, 2, 2, 3, 47.
- Factorize\( (540) = \) \(1\times 2\times 2\times 3\times 3\times 3\times 5\)
- Factorize\( (9024) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 47\)
Now we need to find any which are common for each number (1, 2, 2, 3) and multiply these numbers together.
\(GCF(540, 9024) = 1\times 2\times 2\times 3 = 12\).
Greatest Common Factor of 540 and 9024 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 9024 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 47, 48, 64, 94, 96, 141, 188, 192, 282, 376, 564, 752, 1128, 1504, 2256, 3008, 4512, 9024
As you can see, 12 is the greatest and common number that 540 and 9024 divides into.
So the greatest common factor 540 and 9024 is 12.
\(GCF(540, 9024) = 12\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
