What is the Greatest Common Factor of 25961 and 25974?

Greatest common factor (GCF) of 25961 and 25974 is 13.

GCF(25961,25974) = 13

We will now calculate the prime factors of 25961 and 25974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25961 and 25974.

How to find the GCF of 25961 and 25974?

We will first find the prime factorization of 25961 and 25974. After we will calculate the factors of 25961 and 25974 and find the biggest common factor number .

Step-1: Prime Factorization of 25961

Prime factors of 25961 are 13, 1997. Prime factorization of 25961 in exponential form is:

25961 = 13¹ × 1997¹

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 25961

List of positive integer factors of 25961 that divides 25961 without a remainder.

1, 13, 1997

Step-4: Factors of 25974

List of positive integer factors of 25974 that divides 25961 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 25961 and 25974. The biggest common factor number is the GCF number.
So the greatest common factor 25961 and 25974 is 13.

Also check out the Least Common Multiple of 25961 and 25974