What is the Greatest Common Factor of 9660 and 9675?

Greatest common factor (GCF) of 9660 and 9675 is 15.

GCF(9660,9675) = 15

We will now calculate the prime factors of 9660 and 9675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9660 and 9675.

How to find the GCF of 9660 and 9675?

We will first find the prime factorization of 9660 and 9675. After we will calculate the factors of 9660 and 9675 and find the biggest common factor number .

Step-1: Prime Factorization of 9660

Prime factors of 9660 are 2, 3, 5, 7, 23. Prime factorization of 9660 in exponential form is:

9660 = 2² × 3¹ × 5¹ × 7¹ × 23¹

Step-2: 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-3: Factors of 9660

List of positive integer factors of 9660 that divides 9660 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 28, 30, 35, 42, 46, 60, 69, 70, 84, 92, 105, 115, 138, 140, 161, 210, 230, 276, 322, 345, 420, 460, 483, 644, 690, 805, 966, 1380, 1610, 1932, 2415, 3220, 4830

Step-4: Factors of 9675

List of positive integer factors of 9675 that divides 9660 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9660 and 9675. The biggest common factor number is the GCF number.
So the greatest common factor 9660 and 9675 is 15.

Also check out the Least Common Multiple of 9660 and 9675