What is the Greatest Common Factor of 26586 and 26600?

Greatest common factor (GCF) of 26586 and 26600 is 14.

GCF(26586,26600) = 14

We will now calculate the prime factors of 26586 and 26600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26586 and 26600.

How to find the GCF of 26586 and 26600?

We will first find the prime factorization of 26586 and 26600. After we will calculate the factors of 26586 and 26600 and find the biggest common factor number .

Step-1: Prime Factorization of 26586

Prime factors of 26586 are 2, 3, 7, 211. Prime factorization of 26586 in exponential form is:

26586 = 2¹ × 3² × 7¹ × 211¹

Step-2: Prime Factorization of 26600

Prime factors of 26600 are 2, 5, 7, 19. Prime factorization of 26600 in exponential form is:

26600 = 2³ × 5² × 7¹ × 19¹

Step-3: Factors of 26586

List of positive integer factors of 26586 that divides 26586 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 211, 422, 633, 1266, 1477, 1899, 2954, 3798, 4431, 8862, 13293

Step-4: Factors of 26600

List of positive integer factors of 26600 that divides 26586 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 19, 20, 25, 28, 35, 38, 40, 50, 56, 70, 76, 95, 100, 133, 140, 152, 175, 190, 200, 266, 280, 350, 380, 475, 532, 665, 700, 760, 950, 1064, 1330, 1400, 1900, 2660, 3325, 3800, 5320, 6650, 13300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26586 and 26600. The biggest common factor number is the GCF number.
So the greatest common factor 26586 and 26600 is 14.

Also check out the Least Common Multiple of 26586 and 26600