What is the Greatest Common Factor of 25856 and 25872?

Greatest common factor (GCF) of 25856 and 25872 is 16.

GCF(25856,25872) = 16

We will now calculate the prime factors of 25856 and 25872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25856 and 25872.

How to find the GCF of 25856 and 25872?

We will first find the prime factorization of 25856 and 25872. After we will calculate the factors of 25856 and 25872 and find the biggest common factor number .

Step-1: Prime Factorization of 25856

Prime factors of 25856 are 2, 101. Prime factorization of 25856 in exponential form is:

25856 = 2⁸ × 101¹

Step-2: Prime Factorization of 25872

Prime factors of 25872 are 2, 3, 7, 11. Prime factorization of 25872 in exponential form is:

25872 = 2⁴ × 3¹ × 7² × 11¹

Step-3: Factors of 25856

List of positive integer factors of 25856 that divides 25856 without a remainder.

1, 2, 4, 8, 16, 32, 64, 101, 128, 202, 256, 404, 808, 1616, 3232, 6464, 12928

Step-4: Factors of 25872

List of positive integer factors of 25872 that divides 25856 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 33, 42, 44, 48, 49, 56, 66, 77, 84, 88, 98, 112, 132, 147, 154, 168, 176, 196, 231, 264, 294, 308, 336, 392, 462, 528, 539, 588, 616, 784, 924, 1078, 1176, 1232, 1617, 1848, 2156, 2352, 3234, 3696, 4312, 6468, 8624, 12936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25856 and 25872. The biggest common factor number is the GCF number.
So the greatest common factor 25856 and 25872 is 16.

Also check out the Least Common Multiple of 25856 and 25872