What is the Greatest Common Factor of 25905 and 25914?

Greatest common factor (GCF) of 25905 and 25914 is 3.

GCF(25905,25914) = 3

We will now calculate the prime factors of 25905 and 25914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25905 and 25914.

How to find the GCF of 25905 and 25914?

We will first find the prime factorization of 25905 and 25914. After we will calculate the factors of 25905 and 25914 and find the biggest common factor number .

Step-1: Prime Factorization of 25905

Prime factors of 25905 are 3, 5, 11, 157. Prime factorization of 25905 in exponential form is:

25905 = 3¹ × 5¹ × 11¹ × 157¹

Step-2: 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-3: Factors of 25905

List of positive integer factors of 25905 that divides 25905 without a remainder.

1, 3, 5, 11, 15, 33, 55, 157, 165, 471, 785, 1727, 2355, 5181, 8635

Step-4: Factors of 25914

List of positive integer factors of 25914 that divides 25905 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25905 and 25914. The biggest common factor number is the GCF number.
So the greatest common factor 25905 and 25914 is 3.

Also check out the Least Common Multiple of 25905 and 25914