What is the Greatest Common Factor of 9675 and 9685?

Greatest common factor (GCF) of 9675 and 9685 is 5.

GCF(9675,9685) = 5

We will now calculate the prime factors of 9675 and 9685, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9675 and 9685.

How to find the GCF of 9675 and 9685?

We will first find the prime factorization of 9675 and 9685. After we will calculate the factors of 9675 and 9685 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 9685

Prime factors of 9685 are 5, 13, 149. Prime factorization of 9685 in exponential form is:

9685 = 5¹ × 13¹ × 149¹

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 9685

List of positive integer factors of 9685 that divides 9675 without a remainder.

1, 5, 13, 65, 149, 745, 1937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9675 and 9685. The biggest common factor number is the GCF number.
So the greatest common factor 9675 and 9685 is 5.

Also check out the Least Common Multiple of 9675 and 9685