Greatest Common Factor of 144 and 189
GCF(144, 189) = 9, Greatest common factor of 144 and 189 is 9. 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 144 and 189. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 144 and 189 by prime factorization method
We will first find the prime factorization of 144 and 189.
Prime Factorization of 144 is 1, 2, 2, 2, 2, 3, 3 and Prime Factorization of 189 is 1, 3, 3, 3, 7.
- Factorize\( (144) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 3\)
- Factorize\( (189) = \) \(1\times 3\times 3\times 3\times 7\)
Now we need to find any which are common for each number (1, 3, 3) and multiply these numbers together.
\(GCF(144, 189) = 1\times 3\times 3 = 9\).
Greatest Common Factor of 144 and 189 by matching factors method
List of positive integers factors of 144 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
List of positive integers factors of 189 leaving a remainder zero is 1, 3, 7, 9, 21, 27, 63, 189
As you can see, 9 is the greatest and common number that 144 and 189 divides into.
So the greatest common factor 144 and 189 is 9.
\(GCF(144, 189) = 9\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
