Greatest Common Factor of 144 and 9828
GCF(144, 9828) = 36, Greatest common factor of 144 and 9828 is 36. 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 144 and 9828. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 144 and 9828 by prime factorization method
We will first find the prime factorization of 144 and 9828.
Prime Factorization of 144 is 1, 2, 2, 2, 2, 3, 3 and Prime Factorization of 9828 is 1, 2, 2, 3, 3, 3, 7, 13.
- Factorize\( (144) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 3\)
- Factorize\( (9828) = \) \(1\times 2\times 2\times 3\times 3\times 3\times 7\times 13\)
Now we need to find any which are common for each number (1, 2, 2, 3, 3) and multiply these numbers together.
\(GCF(144, 9828) = 1\times 2\times 2\times 3\times 3 = 36\).
Greatest Common Factor of 144 and 9828 by matching factors method
List of positive integers factors of 144 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
List of positive integers factors of 9828 leaving a remainder zero is 1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 26, 27, 28, 36, 39, 42, 52, 54, 63, 78, 84, 91, 108, 117, 126, 156, 182, 189, 234, 252, 273, 351, 364, 378, 468, 546, 702, 756, 819, 1092, 1404, 1638, 2457, 3276, 4914, 9828
As you can see, 36 is the greatest and common number that 144 and 9828 divides into.
So the greatest common factor 144 and 9828 is 36.
\(GCF(144, 9828) = 36\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
