What is the Greatest Common Factor of 25857 and 25874?

Greatest common factor (GCF) of 25857 and 25874 is 17.

GCF(25857,25874) = 17

We will now calculate the prime factors of 25857 and 25874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25857 and 25874.

How to find the GCF of 25857 and 25874?

We will first find the prime factorization of 25857 and 25874. After we will calculate the factors of 25857 and 25874 and find the biggest common factor number .

Step-1: Prime Factorization of 25857

Prime factors of 25857 are 3, 13, 17. Prime factorization of 25857 in exponential form is:

25857 = 3² × 13² × 17¹

Step-2: Prime Factorization of 25874

Prime factors of 25874 are 2, 17, 761. Prime factorization of 25874 in exponential form is:

25874 = 2¹ × 17¹ × 761¹

Step-3: Factors of 25857

List of positive integer factors of 25857 that divides 25857 without a remainder.

1, 3, 9, 13, 17, 39, 51, 117, 153, 169, 221, 507, 663, 1521, 1989, 2873, 8619

Step-4: Factors of 25874

List of positive integer factors of 25874 that divides 25857 without a remainder.

1, 2, 17, 34, 761, 1522, 12937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25857 and 25874. The biggest common factor number is the GCF number.
So the greatest common factor 25857 and 25874 is 17.

Also check out the Least Common Multiple of 25857 and 25874