What is the Greatest Common Factor of 25802 and 25814?

Greatest common factor (GCF) of 25802 and 25814 is 2.

GCF(25802,25814) = 2

We will now calculate the prime factors of 25802 and 25814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25802 and 25814.

How to find the GCF of 25802 and 25814?

We will first find the prime factorization of 25802 and 25814. After we will calculate the factors of 25802 and 25814 and find the biggest common factor number .

Step-1: Prime Factorization of 25802

Prime factors of 25802 are 2, 7, 19, 97. Prime factorization of 25802 in exponential form is:

25802 = 2¹ × 7¹ × 19¹ × 97¹

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 25802

List of positive integer factors of 25802 that divides 25802 without a remainder.

1, 2, 7, 14, 19, 38, 97, 133, 194, 266, 679, 1358, 1843, 3686, 12901

Step-4: Factors of 25814

List of positive integer factors of 25814 that divides 25802 without a remainder.

1, 2, 12907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25802 and 25814. The biggest common factor number is the GCF number.
So the greatest common factor 25802 and 25814 is 2.

Also check out the Least Common Multiple of 25802 and 25814