What is the Greatest Common Factor of 25974 and 25983?

Greatest common factor (GCF) of 25974 and 25983 is 9.

GCF(25974,25983) = 9

We will now calculate the prime factors of 25974 and 25983, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25974 and 25983.

How to find the GCF of 25974 and 25983?

We will first find the prime factorization of 25974 and 25983. After we will calculate the factors of 25974 and 25983 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 25983

Prime factors of 25983 are 3, 2887. Prime factorization of 25983 in exponential form is:

25983 = 3² × 2887¹

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 25983

List of positive integer factors of 25983 that divides 25974 without a remainder.

1, 3, 9, 2887, 8661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25974 and 25983. The biggest common factor number is the GCF number.
So the greatest common factor 25974 and 25983 is 9.

Also check out the Least Common Multiple of 25974 and 25983