What is the Greatest Common Factor of 25854 and 25872?

Greatest common factor (GCF) of 25854 and 25872 is 6.

GCF(25854,25872) = 6

We will now calculate the prime factors of 25854 and 25872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25854 and 25872.

How to find the GCF of 25854 and 25872?

We will first find the prime factorization of 25854 and 25872. After we will calculate the factors of 25854 and 25872 and find the biggest common factor number .

Step-1: Prime Factorization of 25854

Prime factors of 25854 are 2, 3, 31, 139. Prime factorization of 25854 in exponential form is:

25854 = 2¹ × 3¹ × 31¹ × 139¹

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 25854

List of positive integer factors of 25854 that divides 25854 without a remainder.

1, 2, 3, 6, 31, 62, 93, 139, 186, 278, 417, 834, 4309, 8618, 12927

Step-4: Factors of 25872

List of positive integer factors of 25872 that divides 25854 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 25854 and 25872. The biggest common factor number is the GCF number.
So the greatest common factor 25854 and 25872 is 6.

Also check out the Least Common Multiple of 25854 and 25872