What is the Greatest Common Factor of 288 and 300?

Greatest common factor (GCF) of 288 and 300 is 12.

GCF(288,300) = 12

We will now calculate the prime factors of 288 and 300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 288 and 300.

How to find the GCF of 288 and 300?

We will first find the prime factorization of 288 and 300. After we will calculate the factors of 288 and 300 and find the biggest common factor number .

Step-1: Prime Factorization of 288

Prime factors of 288 are 2, 3. Prime factorization of 288 in exponential form is:

288 = 2⁵ × 3²

Step-2: Prime Factorization of 300

Prime factors of 300 are 2, 3, 5. Prime factorization of 300 in exponential form is:

300 = 2² × 3¹ × 5²

Step-3: Factors of 288

List of positive integer factors of 288 that divides 288 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144

Step-4: Factors of 300

List of positive integer factors of 300 that divides 288 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 288 and 300. The biggest common factor number is the GCF number.
So the greatest common factor 288 and 300 is 12.

Also check out the Least Common Multiple of 288 and 300