Greatest Common Factor of 120 and 9744
GCF(120, 9744) = 24, Greatest common factor of 120 and 9744 is 24. 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 120 and 9744. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 120 and 9744 by prime factorization method
We will first find the prime factorization of 120 and 9744.
Prime Factorization of 120 is 1, 2, 2, 2, 3, 5 and Prime Factorization of 9744 is 1, 2, 2, 2, 2, 3, 7, 29.
- Factorize\( (120) = \) \(1\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (9744) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 7\times 29\)
Now we need to find any which are common for each number (1, 2, 2, 2, 3) and multiply these numbers together.
\(GCF(120, 9744) = 1\times 2\times 2\times 2\times 3 = 24\).
Greatest Common Factor of 120 and 9744 by matching factors method
List of positive integers factors of 120 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
List of positive integers factors of 9744 leaving a remainder zero is 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 42, 48, 56, 58, 84, 87, 112, 116, 168, 174, 203, 232, 336, 348, 406, 464, 609, 696, 812, 1218, 1392, 1624, 2436, 3248, 4872, 9744
As you can see, 24 is the greatest and common number that 120 and 9744 divides into.
So the greatest common factor 120 and 9744 is 24.
\(GCF(120, 9744) = 24\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
