What is the Greatest Common Factor of 25734 and 25749?

Greatest common factor (GCF) of 25734 and 25749 is 3.

GCF(25734,25749) = 3

We will now calculate the prime factors of 25734 and 25749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25734 and 25749.

How to find the GCF of 25734 and 25749?

We will first find the prime factorization of 25734 and 25749. After we will calculate the factors of 25734 and 25749 and find the biggest common factor number .

Step-1: Prime Factorization of 25734

Prime factors of 25734 are 2, 3, 4289. Prime factorization of 25734 in exponential form is:

25734 = 2¹ × 3¹ × 4289¹

Step-2: Prime Factorization of 25749

Prime factors of 25749 are 3, 2861. Prime factorization of 25749 in exponential form is:

25749 = 3² × 2861¹

Step-3: Factors of 25734

List of positive integer factors of 25734 that divides 25734 without a remainder.

1, 2, 3, 6, 4289, 8578, 12867

Step-4: Factors of 25749

List of positive integer factors of 25749 that divides 25734 without a remainder.

1, 3, 9, 2861, 8583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25734 and 25749. The biggest common factor number is the GCF number.
So the greatest common factor 25734 and 25749 is 3.

Also check out the Least Common Multiple of 25734 and 25749