What is the Greatest Common Factor of 25974 and 25987?

Greatest common factor (GCF) of 25974 and 25987 is 13.

GCF(25974,25987) = 13

We will now calculate the prime factors of 25974 and 25987, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25974 and 25987.

How to find the GCF of 25974 and 25987?

We will first find the prime factorization of 25974 and 25987. After we will calculate the factors of 25974 and 25987 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 25987

Prime factors of 25987 are 13, 1999. Prime factorization of 25987 in exponential form is:

25987 = 13¹ × 1999¹

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 25987

List of positive integer factors of 25987 that divides 25974 without a remainder.

1, 13, 1999

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25974 and 25987. The biggest common factor number is the GCF number.
So the greatest common factor 25974 and 25987 is 13.

Also check out the Least Common Multiple of 25974 and 25987