What is the Greatest Common Factor of 25674 and 25689?

Greatest common factor (GCF) of 25674 and 25689 is 3.

GCF(25674,25689) = 3

We will now calculate the prime factors of 25674 and 25689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25674 and 25689.

How to find the GCF of 25674 and 25689?

We will first find the prime factorization of 25674 and 25689. After we will calculate the factors of 25674 and 25689 and find the biggest common factor number .

Step-1: Prime Factorization of 25674

Prime factors of 25674 are 2, 3, 11, 389. Prime factorization of 25674 in exponential form is:

25674 = 2¹ × 3¹ × 11¹ × 389¹

Step-2: Prime Factorization of 25689

Prime factors of 25689 are 3, 8563. Prime factorization of 25689 in exponential form is:

25689 = 3¹ × 8563¹

Step-3: Factors of 25674

List of positive integer factors of 25674 that divides 25674 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 389, 778, 1167, 2334, 4279, 8558, 12837

Step-4: Factors of 25689

List of positive integer factors of 25689 that divides 25674 without a remainder.

1, 3, 8563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25674 and 25689. The biggest common factor number is the GCF number.
So the greatest common factor 25674 and 25689 is 3.

Also check out the Least Common Multiple of 25674 and 25689