What is the Greatest Common Factor of 25974 and 25989?

Greatest common factor (GCF) of 25974 and 25989 is 3.

GCF(25974,25989) = 3

We will now calculate the prime factors of 25974 and 25989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25974 and 25989.

How to find the GCF of 25974 and 25989?

We will first find the prime factorization of 25974 and 25989. After we will calculate the factors of 25974 and 25989 and find the biggest common factor number .

Step-1: Prime Factorization of 25974

Prime factors of 25974 are 2, 3, 13, 37. Prime factorization of 25974 in exponential form is:

25974 = 2¹ × 3³ × 13¹ × 37¹

Step-2: Prime Factorization of 25989

Prime factors of 25989 are 3, 8663. Prime factorization of 25989 in exponential form is:

25989 = 3¹ × 8663¹

Step-3: Factors of 25974

List of positive integer factors of 25974 that divides 25974 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 37, 39, 54, 74, 78, 111, 117, 222, 234, 333, 351, 481, 666, 702, 962, 999, 1443, 1998, 2886, 4329, 8658, 12987

Step-4: Factors of 25989

List of positive integer factors of 25989 that divides 25974 without a remainder.

1, 3, 8663

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25974 and 25989. The biggest common factor number is the GCF number.
So the greatest common factor 25974 and 25989 is 3.

Also check out the Least Common Multiple of 25974 and 25989