What is the Greatest Common Factor of 9584 and 9600?

Greatest common factor (GCF) of 9584 and 9600 is 16.

GCF(9584,9600) = 16

We will now calculate the prime factors of 9584 and 9600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9584 and 9600.

How to find the GCF of 9584 and 9600?

We will first find the prime factorization of 9584 and 9600. After we will calculate the factors of 9584 and 9600 and find the biggest common factor number .

Step-1: Prime Factorization of 9584

Prime factors of 9584 are 2, 599. Prime factorization of 9584 in exponential form is:

9584 = 2⁴ × 599¹

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 9584

List of positive integer factors of 9584 that divides 9584 without a remainder.

1, 2, 4, 8, 16, 599, 1198, 2396, 4792

Step-4: Factors of 9600

List of positive integer factors of 9600 that divides 9584 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 9584 and 9600. The biggest common factor number is the GCF number.
So the greatest common factor 9584 and 9600 is 16.

Also check out the Least Common Multiple of 9584 and 9600