What is the Greatest Common Factor of 9675 and 9680?

Greatest common factor (GCF) of 9675 and 9680 is 5.

GCF(9675,9680) = 5

We will now calculate the prime factors of 9675 and 9680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9675 and 9680.

How to find the GCF of 9675 and 9680?

We will first find the prime factorization of 9675 and 9680. After we will calculate the factors of 9675 and 9680 and find the biggest common factor number .

Step-1: Prime Factorization of 9675

Prime factors of 9675 are 3, 5, 43. Prime factorization of 9675 in exponential form is:

9675 = 3² × 5² × 43¹

Step-2: Prime Factorization of 9680

Prime factors of 9680 are 2, 5, 11. Prime factorization of 9680 in exponential form is:

9680 = 2⁴ × 5¹ × 11²

Step-3: Factors of 9675

List of positive integer factors of 9675 that divides 9675 without a remainder.

1, 3, 5, 9, 15, 25, 43, 45, 75, 129, 215, 225, 387, 645, 1075, 1935, 3225

Step-4: Factors of 9680

List of positive integer factors of 9680 that divides 9675 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 121, 176, 220, 242, 440, 484, 605, 880, 968, 1210, 1936, 2420, 4840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9675 and 9680. The biggest common factor number is the GCF number.
So the greatest common factor 9675 and 9680 is 5.

Also check out the Least Common Multiple of 9675 and 9680