What is the Greatest Common Factor of 25789 and 25806?

Greatest common factor (GCF) of 25789 and 25806 is 17.

GCF(25789,25806) = 17

We will now calculate the prime factors of 25789 and 25806, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25789 and 25806.

How to find the GCF of 25789 and 25806?

We will first find the prime factorization of 25789 and 25806. After we will calculate the factors of 25789 and 25806 and find the biggest common factor number .

Step-1: Prime Factorization of 25789

Prime factors of 25789 are 17, 37, 41. Prime factorization of 25789 in exponential form is:

25789 = 17¹ × 37¹ × 41¹

Step-2: Prime Factorization of 25806

Prime factors of 25806 are 2, 3, 11, 17, 23. Prime factorization of 25806 in exponential form is:

25806 = 2¹ × 3¹ × 11¹ × 17¹ × 23¹

Step-3: Factors of 25789

List of positive integer factors of 25789 that divides 25789 without a remainder.

1, 17, 37, 41, 629, 697, 1517

Step-4: Factors of 25806

List of positive integer factors of 25806 that divides 25789 without a remainder.

1, 2, 3, 6, 11, 17, 22, 23, 33, 34, 46, 51, 66, 69, 102, 138, 187, 253, 374, 391, 506, 561, 759, 782, 1122, 1173, 1518, 2346, 4301, 8602, 12903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25789 and 25806. The biggest common factor number is the GCF number.
So the greatest common factor 25789 and 25806 is 17.

Also check out the Least Common Multiple of 25789 and 25806