Greatest Common Factor of 84 and 708
GCF(84, 708) = 12, Greatest common factor of 84 and 708 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 84 and 708. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 84 and 708 by prime factorization method
We will first find the prime factorization of 84 and 708.
Prime Factorization of 84 is 1, 2, 2, 3, 7 and Prime Factorization of 708 is 1, 2, 2, 3, 59.
- Factorize\( (84) = \) \(1\times 2\times 2\times 3\times 7\)
- Factorize\( (708) = \) \(1\times 2\times 2\times 3\times 59\)
Now we need to find any which are common for each number (1, 2, 2, 3) and multiply these numbers together.
\(GCF(84, 708) = 1\times 2\times 2\times 3 = 12\).
Greatest Common Factor of 84 and 708 by matching factors method
List of positive integers factors of 84 leaving a remainder zero is 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
List of positive integers factors of 708 leaving a remainder zero is 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
As you can see, 12 is the greatest and common number that 84 and 708 divides into.
So the greatest common factor 84 and 708 is 12.
\(GCF(84, 708) = 12\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
