What is the Greatest Common Factor of 25965 and 25974?

Greatest common factor (GCF) of 25965 and 25974 is 9.

GCF(25965,25974) = 9

We will now calculate the prime factors of 25965 and 25974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25965 and 25974.

How to find the GCF of 25965 and 25974?

We will first find the prime factorization of 25965 and 25974. After we will calculate the factors of 25965 and 25974 and find the biggest common factor number .

Step-1: Prime Factorization of 25965

Prime factors of 25965 are 3, 5, 577. Prime factorization of 25965 in exponential form is:

25965 = 3² × 5¹ × 577¹

Step-2: 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-3: Factors of 25965

List of positive integer factors of 25965 that divides 25965 without a remainder.

1, 3, 5, 9, 15, 45, 577, 1731, 2885, 5193, 8655

Step-4: Factors of 25974

List of positive integer factors of 25974 that divides 25965 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25965 and 25974. The biggest common factor number is the GCF number.
So the greatest common factor 25965 and 25974 is 9.

Also check out the Least Common Multiple of 25965 and 25974