What is the Greatest Common Factor of 32085 and 32100?

Greatest common factor (GCF) of 32085 and 32100 is 15.

GCF(32085,32100) = 15

We will now calculate the prime factors of 32085 and 32100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32085 and 32100.

How to find the GCF of 32085 and 32100?

We will first find the prime factorization of 32085 and 32100. After we will calculate the factors of 32085 and 32100 and find the biggest common factor number .

Step-1: Prime Factorization of 32085

Prime factors of 32085 are 3, 5, 23, 31. Prime factorization of 32085 in exponential form is:

32085 = 3² × 5¹ × 23¹ × 31¹

Step-2: Prime Factorization of 32100

Prime factors of 32100 are 2, 3, 5, 107. Prime factorization of 32100 in exponential form is:

32100 = 2² × 3¹ × 5² × 107¹

Step-3: Factors of 32085

List of positive integer factors of 32085 that divides 32085 without a remainder.

1, 3, 5, 9, 15, 23, 31, 45, 69, 93, 115, 155, 207, 279, 345, 465, 713, 1035, 1395, 2139, 3565, 6417, 10695

Step-4: Factors of 32100

List of positive integer factors of 32100 that divides 32085 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 107, 150, 214, 300, 321, 428, 535, 642, 1070, 1284, 1605, 2140, 2675, 3210, 5350, 6420, 8025, 10700, 16050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32085 and 32100. The biggest common factor number is the GCF number.
So the greatest common factor 32085 and 32100 is 15.

Also check out the Least Common Multiple of 32085 and 32100