Greatest Common Factor of 132 and 1683
GCF(132, 1683) = 33, Greatest common factor of 132 and 1683 is 33. 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 132 and 1683. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 132 and 1683 by prime factorization method
We will first find the prime factorization of 132 and 1683.
Prime Factorization of 132 is 1, 2, 2, 3, 11 and Prime Factorization of 1683 is 1, 3, 3, 11, 17.
- Factorize\( (132) = \) \(1\times 2\times 2\times 3\times 11\)
- Factorize\( (1683) = \) \(1\times 3\times 3\times 11\times 17\)
Now we need to find any which are common for each number (1, 3, 11) and multiply these numbers together.
\(GCF(132, 1683) = 1\times 3\times 11 = 33\).
Greatest Common Factor of 132 and 1683 by matching factors method
List of positive integers factors of 132 leaving a remainder zero is 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
List of positive integers factors of 1683 leaving a remainder zero is 1, 3, 9, 11, 17, 33, 51, 99, 153, 187, 561, 1683
As you can see, 33 is the greatest and common number that 132 and 1683 divides into.
So the greatest common factor 132 and 1683 is 33.
\(GCF(132, 1683) = 33\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
