What is the Greatest Common Factor of 25806 and 25814?

Greatest common factor (GCF) of 25806 and 25814 is 2.

GCF(25806,25814) = 2

We will now calculate the prime factors of 25806 and 25814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25806 and 25814.

How to find the GCF of 25806 and 25814?

We will first find the prime factorization of 25806 and 25814. After we will calculate the factors of 25806 and 25814 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 25814

Prime factors of 25814 are 2, 12907. Prime factorization of 25814 in exponential form is:

25814 = 2¹ × 12907¹

Step-3: Factors of 25806

List of positive integer factors of 25806 that divides 25806 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

Step-4: Factors of 25814

List of positive integer factors of 25814 that divides 25806 without a remainder.

1, 2, 12907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25806 and 25814. The biggest common factor number is the GCF number.
So the greatest common factor 25806 and 25814 is 2.

Also check out the Least Common Multiple of 25806 and 25814