What is the Greatest Common Factor of 25586 and 25600?

Greatest common factor (GCF) of 25586 and 25600 is 2.

GCF(25586,25600) = 2

We will now calculate the prime factors of 25586 and 25600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25586 and 25600.

How to find the GCF of 25586 and 25600?

We will first find the prime factorization of 25586 and 25600. After we will calculate the factors of 25586 and 25600 and find the biggest common factor number .

Step-1: Prime Factorization of 25586

Prime factors of 25586 are 2, 11, 1163. Prime factorization of 25586 in exponential form is:

25586 = 2¹ × 11¹ × 1163¹

Step-2: Prime Factorization of 25600

Prime factors of 25600 are 2, 5. Prime factorization of 25600 in exponential form is:

25600 = 2¹⁰ × 5²

Step-3: Factors of 25586

List of positive integer factors of 25586 that divides 25586 without a remainder.

1, 2, 11, 22, 1163, 2326, 12793

Step-4: Factors of 25600

List of positive integer factors of 25600 that divides 25586 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25586 and 25600. The biggest common factor number is the GCF number.
So the greatest common factor 25586 and 25600 is 2.

Also check out the Least Common Multiple of 25586 and 25600