What is the Greatest Common Factor of 9600 and 9614?

Greatest common factor (GCF) of 9600 and 9614 is 2.

GCF(9600,9614) = 2

We will now calculate the prime factors of 9600 and 9614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9600 and 9614.

How to find the GCF of 9600 and 9614?

We will first find the prime factorization of 9600 and 9614. After we will calculate the factors of 9600 and 9614 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 9614

Prime factors of 9614 are 2, 11, 19, 23. Prime factorization of 9614 in exponential form is:

9614 = 2¹ × 11¹ × 19¹ × 23¹

Step-3: Factors of 9600

List of positive integer factors of 9600 that divides 9600 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

Step-4: Factors of 9614

List of positive integer factors of 9614 that divides 9600 without a remainder.

1, 2, 11, 19, 22, 23, 38, 46, 209, 253, 418, 437, 506, 874, 4807

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9600 and 9614. The biggest common factor number is the GCF number.
So the greatest common factor 9600 and 9614 is 2.

Also check out the Least Common Multiple of 9600 and 9614