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