What is the Greatest Common Factor of 25749 and 25764?

Greatest common factor (GCF) of 25749 and 25764 is 3.

GCF(25749,25764) = 3

We will now calculate the prime factors of 25749 and 25764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25749 and 25764.

How to find the GCF of 25749 and 25764?

We will first find the prime factorization of 25749 and 25764. After we will calculate the factors of 25749 and 25764 and find the biggest common factor number .

Step-1: Prime Factorization of 25749

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

25749 = 3² × 2861¹

Step-2: Prime Factorization of 25764

Prime factors of 25764 are 2, 3, 19, 113. Prime factorization of 25764 in exponential form is:

25764 = 2² × 3¹ × 19¹ × 113¹

Step-3: Factors of 25749

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

1, 3, 9, 2861, 8583

Step-4: Factors of 25764

List of positive integer factors of 25764 that divides 25749 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 113, 114, 226, 228, 339, 452, 678, 1356, 2147, 4294, 6441, 8588, 12882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25749 and 25764. The biggest common factor number is the GCF number.
So the greatest common factor 25749 and 25764 is 3.

Also check out the Least Common Multiple of 25749 and 25764