Greatest Common Factor of 76 and 9600
GCF(76, 9600) = 4, Greatest common factor of 76 and 9600 is 4. 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 76 and 9600. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 76 and 9600 by prime factorization method
We will first find the prime factorization of 76 and 9600.
Prime Factorization of 76 is 1, 2, 2, 19 and Prime Factorization of 9600 is 1, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5.
- Factorize\( (76) = \) \(1\times 2\times 2\times 19\)
- Factorize\( (9600) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 2) and multiply these numbers together.
\(GCF(76, 9600) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 76 and 9600 by matching factors method
List of positive integers factors of 76 leaving a remainder zero is 1, 2, 4, 19, 38, 76
List of positive integers factors of 9600 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600
As you can see, 4 is the greatest and common number that 76 and 9600 divides into.
So the greatest common factor 76 and 9600 is 4.
\(GCF(76, 9600) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
