What is the Greatest Common Factor of 26085 and 26100?

Greatest common factor (GCF) of 26085 and 26100 is 15.

GCF(26085,26100) = 15

We will now calculate the prime factors of 26085 and 26100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26085 and 26100.

How to find the GCF of 26085 and 26100?

We will first find the prime factorization of 26085 and 26100. After we will calculate the factors of 26085 and 26100 and find the biggest common factor number .

Step-1: Prime Factorization of 26085

Prime factors of 26085 are 3, 5, 37, 47. Prime factorization of 26085 in exponential form is:

26085 = 3¹ × 5¹ × 37¹ × 47¹

Step-2: Prime Factorization of 26100

Prime factors of 26100 are 2, 3, 5, 29. Prime factorization of 26100 in exponential form is:

26100 = 2² × 3² × 5² × 29¹

Step-3: Factors of 26085

List of positive integer factors of 26085 that divides 26085 without a remainder.

1, 3, 5, 15, 37, 47, 111, 141, 185, 235, 555, 705, 1739, 5217, 8695

Step-4: Factors of 26100

List of positive integer factors of 26100 that divides 26085 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 29, 30, 36, 45, 50, 58, 60, 75, 87, 90, 100, 116, 145, 150, 174, 180, 225, 261, 290, 300, 348, 435, 450, 522, 580, 725, 870, 900, 1044, 1305, 1450, 1740, 2175, 2610, 2900, 4350, 5220, 6525, 8700, 13050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26085 and 26100. The biggest common factor number is the GCF number.
So the greatest common factor 26085 and 26100 is 15.

Also check out the Least Common Multiple of 26085 and 26100