Greatest Common Factor of 960 and 840
GCF(960, 840) = 120, Greatest common factor of 960 and 840 is 120. 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 960 and 840. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 960 and 840 by prime factorization method
We will first find the prime factorization of 960 and 840.
Prime Factorization of 960 is 1, 2, 2, 2, 2, 2, 2, 3, 5 and Prime Factorization of 840 is 1, 2, 2, 2, 3, 5, 7.
- Factorize\( (960) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (840) = \) \(1\times 2\times 2\times 2\times 3\times 5\times 7\)
Now we need to find any which are common for each number (1, 2, 2, 2, 3, 5) and multiply these numbers together.
\(GCF(960, 840) = 1\times 2\times 2\times 2\times 3\times 5 = 120\).
Greatest Common Factor of 960 and 840 by matching factors method
List of positive integers factors of 960 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
List of positive integers factors of 840 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
As you can see, 120 is the greatest and common number that 960 and 840 divides into.
So the greatest common factor 960 and 840 is 120.
\(GCF(960, 840) = 120\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
