What is the Greatest Common Factor of 288 and 304?

Greatest common factor (GCF) of 288 and 304 is 16.

GCF(288,304) = 16

We will now calculate the prime factors of 288 and 304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 288 and 304.

How to find the GCF of 288 and 304?

We will first find the prime factorization of 288 and 304. After we will calculate the factors of 288 and 304 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 304

Prime factors of 304 are 2, 19. Prime factorization of 304 in exponential form is:

304 = 2⁴ × 19¹

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 304

List of positive integer factors of 304 that divides 288 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 152

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 288 and 304. The biggest common factor number is the GCF number.
So the greatest common factor 288 and 304 is 16.

Also check out the Least Common Multiple of 288 and 304