What is the Greatest Common Factor of 26385 and 26400?

Greatest common factor (GCF) of 26385 and 26400 is 15.

GCF(26385,26400) = 15

We will now calculate the prime factors of 26385 and 26400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26385 and 26400.

How to find the GCF of 26385 and 26400?

We will first find the prime factorization of 26385 and 26400. After we will calculate the factors of 26385 and 26400 and find the biggest common factor number .

Step-1: Prime Factorization of 26385

Prime factors of 26385 are 3, 5, 1759. Prime factorization of 26385 in exponential form is:

26385 = 3¹ × 5¹ × 1759¹

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 26385

List of positive integer factors of 26385 that divides 26385 without a remainder.

1, 3, 5, 15, 1759, 5277, 8795

Step-4: Factors of 26400

List of positive integer factors of 26400 that divides 26385 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 26385 and 26400. The biggest common factor number is the GCF number.
So the greatest common factor 26385 and 26400 is 15.

Also check out the Least Common Multiple of 26385 and 26400