What is the Greatest Common Factor of 2565 and 2584?

Greatest common factor (GCF) of 2565 and 2584 is 19.

GCF(2565,2584) = 19

We will now calculate the prime factors of 2565 and 2584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2565 and 2584.

How to find the GCF of 2565 and 2584?

We will first find the prime factorization of 2565 and 2584. After we will calculate the factors of 2565 and 2584 and find the biggest common factor number .

Step-1: Prime Factorization of 2565

Prime factors of 2565 are 3, 5, 19. Prime factorization of 2565 in exponential form is:

2565 = 3³ × 5¹ × 19¹

Step-2: Prime Factorization of 2584

Prime factors of 2584 are 2, 17, 19. Prime factorization of 2584 in exponential form is:

2584 = 2³ × 17¹ × 19¹

Step-3: Factors of 2565

List of positive integer factors of 2565 that divides 2565 without a remainder.

1, 3, 5, 9, 15, 19, 27, 45, 57, 95, 135, 171, 285, 513, 855

Step-4: Factors of 2584

List of positive integer factors of 2584 that divides 2565 without a remainder.

1, 2, 4, 8, 17, 19, 34, 38, 68, 76, 136, 152, 323, 646, 1292

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2565 and 2584. The biggest common factor number is the GCF number.
So the greatest common factor 2565 and 2584 is 19.

Also check out the Least Common Multiple of 2565 and 2584