What is the Greatest Common Factor of 23085 and 23100?

Greatest common factor (GCF) of 23085 and 23100 is 15.

GCF(23085,23100) = 15

We will now calculate the prime factors of 23085 and 23100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23085 and 23100.

How to find the GCF of 23085 and 23100?

We will first find the prime factorization of 23085 and 23100. After we will calculate the factors of 23085 and 23100 and find the biggest common factor number .

Step-1: Prime Factorization of 23085

Prime factors of 23085 are 3, 5, 19. Prime factorization of 23085 in exponential form is:

23085 = 3⁵ × 5¹ × 19¹

Step-2: Prime Factorization of 23100

Prime factors of 23100 are 2, 3, 5, 7, 11. Prime factorization of 23100 in exponential form is:

23100 = 2² × 3¹ × 5² × 7¹ × 11¹

Step-3: Factors of 23085

List of positive integer factors of 23085 that divides 23085 without a remainder.

1, 3, 5, 9, 15, 19, 27, 45, 57, 81, 95, 135, 171, 243, 285, 405, 513, 855, 1215, 1539, 2565, 4617, 7695

Step-4: Factors of 23100

List of positive integer factors of 23100 that divides 23085 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 20, 21, 22, 25, 28, 30, 33, 35, 42, 44, 50, 55, 60, 66, 70, 75, 77, 84, 100, 105, 110, 132, 140, 150, 154, 165, 175, 210, 220, 231, 275, 300, 308, 330, 350, 385, 420, 462, 525, 550, 660, 700, 770, 825, 924, 1050, 1100, 1155, 1540, 1650, 1925, 2100, 2310, 3300, 3850, 4620, 5775, 7700, 11550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23085 and 23100. The biggest common factor number is the GCF number.
So the greatest common factor 23085 and 23100 is 15.

Also check out the Least Common Multiple of 23085 and 23100