What is the Greatest Common Factor of 17085 and 17100?

Greatest common factor (GCF) of 17085 and 17100 is 15.

GCF(17085,17100) = 15

We will now calculate the prime factors of 17085 and 17100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17085 and 17100.

How to find the GCF of 17085 and 17100?

We will first find the prime factorization of 17085 and 17100. After we will calculate the factors of 17085 and 17100 and find the biggest common factor number .

Step-1: Prime Factorization of 17085

Prime factors of 17085 are 3, 5, 17, 67. Prime factorization of 17085 in exponential form is:

17085 = 3¹ × 5¹ × 17¹ × 67¹

Step-2: Prime Factorization of 17100

Prime factors of 17100 are 2, 3, 5, 19. Prime factorization of 17100 in exponential form is:

17100 = 2² × 3² × 5² × 19¹

Step-3: Factors of 17085

List of positive integer factors of 17085 that divides 17085 without a remainder.

1, 3, 5, 15, 17, 51, 67, 85, 201, 255, 335, 1005, 1139, 3417, 5695

Step-4: Factors of 17100

List of positive integer factors of 17100 that divides 17085 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 225, 228, 285, 300, 342, 380, 450, 475, 570, 684, 855, 900, 950, 1140, 1425, 1710, 1900, 2850, 3420, 4275, 5700, 8550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17085 and 17100. The biggest common factor number is the GCF number.
So the greatest common factor 17085 and 17100 is 15.

Also check out the Least Common Multiple of 17085 and 17100