What is the Greatest Common Factor of 32160 and 32175?

Greatest common factor (GCF) of 32160 and 32175 is 15.

GCF(32160,32175) = 15

We will now calculate the prime factors of 32160 and 32175, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32160 and 32175.

How to find the GCF of 32160 and 32175?

We will first find the prime factorization of 32160 and 32175. After we will calculate the factors of 32160 and 32175 and find the biggest common factor number .

Step-1: Prime Factorization of 32160

Prime factors of 32160 are 2, 3, 5, 67. Prime factorization of 32160 in exponential form is:

32160 = 2⁵ × 3¹ × 5¹ × 67¹

Step-2: 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-3: Factors of 32160

List of positive integer factors of 32160 that divides 32160 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 67, 80, 96, 120, 134, 160, 201, 240, 268, 335, 402, 480, 536, 670, 804, 1005, 1072, 1340, 1608, 2010, 2144, 2680, 3216, 4020, 5360, 6432, 8040, 10720, 16080

Step-4: Factors of 32175

List of positive integer factors of 32175 that divides 32160 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32160 and 32175. The biggest common factor number is the GCF number.
So the greatest common factor 32160 and 32175 is 15.

Also check out the Least Common Multiple of 32160 and 32175