What is the Greatest Common Factor of 9591 and 9600?

Greatest common factor (GCF) of 9591 and 9600 is 3.

GCF(9591,9600) = 3

We will now calculate the prime factors of 9591 and 9600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9591 and 9600.

How to find the GCF of 9591 and 9600?

We will first find the prime factorization of 9591 and 9600. After we will calculate the factors of 9591 and 9600 and find the biggest common factor number .

Step-1: Prime Factorization of 9591

Prime factors of 9591 are 3, 23, 139. Prime factorization of 9591 in exponential form is:

9591 = 3¹ × 23¹ × 139¹

Step-2: Prime Factorization of 9600

Prime factors of 9600 are 2, 3, 5. Prime factorization of 9600 in exponential form is:

9600 = 2⁷ × 3¹ × 5²

Step-3: Factors of 9591

List of positive integer factors of 9591 that divides 9591 without a remainder.

1, 3, 23, 69, 139, 417, 3197

Step-4: Factors of 9600

List of positive integer factors of 9600 that divides 9591 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9591 and 9600. The biggest common factor number is the GCF number.
So the greatest common factor 9591 and 9600 is 3.

Also check out the Least Common Multiple of 9591 and 9600