Greatest Common Factor of 48 and 288
GCF(48, 288) = 48, Greatest common factor of 48 and 288 is 48. 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 48 and 288. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 48 and 288 by prime factorization method
We will first find the prime factorization of 48 and 288.
Prime Factorization of 48 is 1, 2, 2, 2, 2, 3 and Prime Factorization of 288 is 1, 2, 2, 2, 2, 2, 3, 3.
- Factorize\( (48) = \) \(1\times 2\times 2\times 2\times 2\times 3\)
- Factorize\( (288) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 3\times 3\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2, 3) and multiply these numbers together.
\(GCF(48, 288) = 1\times 2\times 2\times 2\times 2\times 3 = 48\).
Greatest Common Factor of 48 and 288 by matching factors method
List of positive integers factors of 48 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
List of positive integers factors of 288 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
As you can see, 48 is the greatest and common number that 48 and 288 divides into.
So the greatest common factor 48 and 288 is 48.
\(GCF(48, 288) = 48\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
