What is the Greatest Common Factor of 25914 and 25929?

Greatest common factor (GCF) of 25914 and 25929 is 3.

GCF(25914,25929) = 3

We will now calculate the prime factors of 25914 and 25929, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25914 and 25929.

How to find the GCF of 25914 and 25929?

We will first find the prime factorization of 25914 and 25929. After we will calculate the factors of 25914 and 25929 and find the biggest common factor number .

Step-1: Prime Factorization of 25914

Prime factors of 25914 are 2, 3, 7, 617. Prime factorization of 25914 in exponential form is:

25914 = 2¹ × 3¹ × 7¹ × 617¹

Step-2: Prime Factorization of 25929

Prime factors of 25929 are 3, 43, 67. Prime factorization of 25929 in exponential form is:

25929 = 3² × 43¹ × 67¹

Step-3: Factors of 25914

List of positive integer factors of 25914 that divides 25914 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 617, 1234, 1851, 3702, 4319, 8638, 12957

Step-4: Factors of 25929

List of positive integer factors of 25929 that divides 25914 without a remainder.

1, 3, 9, 43, 67, 129, 201, 387, 603, 2881, 8643

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25914 and 25929. The biggest common factor number is the GCF number.
So the greatest common factor 25914 and 25929 is 3.

Also check out the Least Common Multiple of 25914 and 25929