What is the Greatest Common Factor of 32175 and 32188?

Greatest common factor (GCF) of 32175 and 32188 is 13.

GCF(32175,32188) = 13

We will now calculate the prime factors of 32175 and 32188, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32175 and 32188.

How to find the GCF of 32175 and 32188?

We will first find the prime factorization of 32175 and 32188. After we will calculate the factors of 32175 and 32188 and find the biggest common factor number .

Step-1: Prime Factorization of 32175

Prime factors of 32175 are 3, 5, 11, 13. Prime factorization of 32175 in exponential form is:

32175 = 3² × 5² × 11¹ × 13¹

Step-2: Prime Factorization of 32188

Prime factors of 32188 are 2, 13, 619. Prime factorization of 32188 in exponential form is:

32188 = 2² × 13¹ × 619¹

Step-3: Factors of 32175

List of positive integer factors of 32175 that divides 32175 without a remainder.

1, 3, 5, 9, 11, 13, 15, 25, 33, 39, 45, 55, 65, 75, 99, 117, 143, 165, 195, 225, 275, 325, 429, 495, 585, 715, 825, 975, 1287, 2145, 2475, 2925, 3575, 6435, 10725

Step-4: Factors of 32188

List of positive integer factors of 32188 that divides 32175 without a remainder.

1, 2, 4, 13, 26, 52, 619, 1238, 2476, 8047, 16094

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32175 and 32188. The biggest common factor number is the GCF number.
So the greatest common factor 32175 and 32188 is 13.

Also check out the Least Common Multiple of 32175 and 32188