What is the Greatest Common Factor of 26389 and 26400?

Greatest common factor (GCF) of 26389 and 26400 is 11.

GCF(26389,26400) = 11

We will now calculate the prime factors of 26389 and 26400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26389 and 26400.

How to find the GCF of 26389 and 26400?

We will first find the prime factorization of 26389 and 26400. After we will calculate the factors of 26389 and 26400 and find the biggest common factor number .

Step-1: Prime Factorization of 26389

Prime factors of 26389 are 11, 2399. Prime factorization of 26389 in exponential form is:

26389 = 11¹ × 2399¹

Step-2: Prime Factorization of 26400

Prime factors of 26400 are 2, 3, 5, 11. Prime factorization of 26400 in exponential form is:

26400 = 2⁵ × 3¹ × 5² × 11¹

Step-3: Factors of 26389

List of positive integer factors of 26389 that divides 26389 without a remainder.

1, 11, 2399

Step-4: Factors of 26400

List of positive integer factors of 26400 that divides 26389 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25, 30, 32, 33, 40, 44, 48, 50, 55, 60, 66, 75, 80, 88, 96, 100, 110, 120, 132, 150, 160, 165, 176, 200, 220, 240, 264, 275, 300, 330, 352, 400, 440, 480, 528, 550, 600, 660, 800, 825, 880, 1056, 1100, 1200, 1320, 1650, 1760, 2200, 2400, 2640, 3300, 4400, 5280, 6600, 8800, 13200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26389 and 26400. The biggest common factor number is the GCF number.
So the greatest common factor 26389 and 26400 is 11.

Also check out the Least Common Multiple of 26389 and 26400