What is the Greatest Common Factor of 25600 and 25614?

Greatest common factor (GCF) of 25600 and 25614 is 2.

GCF(25600,25614) = 2

We will now calculate the prime factors of 25600 and 25614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25600 and 25614.

How to find the GCF of 25600 and 25614?

We will first find the prime factorization of 25600 and 25614. After we will calculate the factors of 25600 and 25614 and find the biggest common factor number .

Step-1: Prime Factorization of 25600

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

25600 = 2¹⁰ × 5²

Step-2: Prime Factorization of 25614

Prime factors of 25614 are 2, 3, 1423. Prime factorization of 25614 in exponential form is:

25614 = 2¹ × 3² × 1423¹

Step-3: Factors of 25600

List of positive integer factors of 25600 that divides 25600 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

Step-4: Factors of 25614

List of positive integer factors of 25614 that divides 25600 without a remainder.

1, 2, 3, 6, 9, 18, 1423, 2846, 4269, 8538, 12807

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25600 and 25614. The biggest common factor number is the GCF number.
So the greatest common factor 25600 and 25614 is 2.

Also check out the Least Common Multiple of 25600 and 25614