What is the Greatest Common Factor of 9675 and 9690?

Greatest common factor (GCF) of 9675 and 9690 is 15.

GCF(9675,9690) = 15

We will now calculate the prime factors of 9675 and 9690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9675 and 9690.

How to find the GCF of 9675 and 9690?

We will first find the prime factorization of 9675 and 9690. After we will calculate the factors of 9675 and 9690 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 9690

Prime factors of 9690 are 2, 3, 5, 17, 19. Prime factorization of 9690 in exponential form is:

9690 = 2¹ × 3¹ × 5¹ × 17¹ × 19¹

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 9690

List of positive integer factors of 9690 that divides 9675 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 19, 30, 34, 38, 51, 57, 85, 95, 102, 114, 170, 190, 255, 285, 323, 510, 570, 646, 969, 1615, 1938, 3230, 4845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9675 and 9690. The biggest common factor number is the GCF number.
So the greatest common factor 9675 and 9690 is 15.

Also check out the Least Common Multiple of 9675 and 9690