What is the Greatest Common Factor of 25974 and 25980?

Greatest common factor (GCF) of 25974 and 25980 is 6.

GCF(25974,25980) = 6

We will now calculate the prime factors of 25974 and 25980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25974 and 25980.

How to find the GCF of 25974 and 25980?

We will first find the prime factorization of 25974 and 25980. After we will calculate the factors of 25974 and 25980 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 25980

Prime factors of 25980 are 2, 3, 5, 433. Prime factorization of 25980 in exponential form is:

25980 = 2² × 3¹ × 5¹ × 433¹

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 25980

List of positive integer factors of 25980 that divides 25974 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 433, 866, 1299, 1732, 2165, 2598, 4330, 5196, 6495, 8660, 12990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25974 and 25980. The biggest common factor number is the GCF number.
So the greatest common factor 25974 and 25980 is 6.

Also check out the Least Common Multiple of 25974 and 25980