What is the Greatest Common Factor of 285 and 304?

Greatest common factor (GCF) of 285 and 304 is 19.

GCF(285,304) = 19

We will now calculate the prime factors of 285 and 304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 285 and 304.

How to find the GCF of 285 and 304?

We will first find the prime factorization of 285 and 304. After we will calculate the factors of 285 and 304 and find the biggest common factor number .

Step-1: Prime Factorization of 285

Prime factors of 285 are 3, 5, 19. Prime factorization of 285 in exponential form is:

285 = 3¹ × 5¹ × 19¹

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 285

List of positive integer factors of 285 that divides 285 without a remainder.

1, 3, 5, 15, 19, 57, 95

Step-4: Factors of 304

List of positive integer factors of 304 that divides 285 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 285 and 304. The biggest common factor number is the GCF number.
So the greatest common factor 285 and 304 is 19.

Also check out the Least Common Multiple of 285 and 304