Greatest Common Factor of 144 and 90
GCF(144, 90) = 18, Greatest common factor of 144 and 90 is 18. 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 90. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 144 and 90 by prime factorization method
We will first find the prime factorization of 144 and 90.
Prime Factorization of 144 is 1, 2, 2, 2, 2, 3, 3 and Prime Factorization of 90 is 1, 2, 3, 3, 5.
- Factorize\( (144) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 3\)
- Factorize\( (90) = \) \(1\times 2\times 3\times 3\times 5\)
Now we need to find any which are common for each number (1, 2, 3, 3) and multiply these numbers together.
\(GCF(144, 90) = 1\times 2\times 3\times 3 = 18\).
Greatest Common Factor of 144 and 90 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 90 leaving a remainder zero is 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
As you can see, 18 is the greatest and common number that 144 and 90 divides into.
So the greatest common factor 144 and 90 is 18.
\(GCF(144, 90) = 18\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
