What is the Greatest Common Factor of 25707 and 25725?

Greatest common factor (GCF) of 25707 and 25725 is 3.

GCF(25707,25725) = 3

We will now calculate the prime factors of 25707 and 25725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25707 and 25725.

How to find the GCF of 25707 and 25725?

We will first find the prime factorization of 25707 and 25725. After we will calculate the factors of 25707 and 25725 and find the biggest common factor number .

Step-1: Prime Factorization of 25707

Prime factors of 25707 are 3, 11, 19, 41. Prime factorization of 25707 in exponential form is:

25707 = 3¹ × 11¹ × 19¹ × 41¹

Step-2: Prime Factorization of 25725

Prime factors of 25725 are 3, 5, 7. Prime factorization of 25725 in exponential form is:

25725 = 3¹ × 5² × 7³

Step-3: Factors of 25707

List of positive integer factors of 25707 that divides 25707 without a remainder.

1, 3, 11, 19, 33, 41, 57, 123, 209, 451, 627, 779, 1353, 2337, 8569

Step-4: Factors of 25725

List of positive integer factors of 25725 that divides 25707 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 343, 525, 735, 1029, 1225, 1715, 3675, 5145, 8575

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25707 and 25725. The biggest common factor number is the GCF number.
So the greatest common factor 25707 and 25725 is 3.

Also check out the Least Common Multiple of 25707 and 25725