What is the Greatest Common Factor of 25289 and 25300?

Greatest common factor (GCF) of 25289 and 25300 is 11.

GCF(25289,25300) = 11

We will now calculate the prime factors of 25289 and 25300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25289 and 25300.

How to find the GCF of 25289 and 25300?

We will first find the prime factorization of 25289 and 25300. After we will calculate the factors of 25289 and 25300 and find the biggest common factor number .

Step-1: Prime Factorization of 25289

Prime factors of 25289 are 11, 19. Prime factorization of 25289 in exponential form is:

25289 = 11³ × 19¹

Step-2: Prime Factorization of 25300

Prime factors of 25300 are 2, 5, 11, 23. Prime factorization of 25300 in exponential form is:

25300 = 2² × 5² × 11¹ × 23¹

Step-3: Factors of 25289

List of positive integer factors of 25289 that divides 25289 without a remainder.

1, 11, 19, 121, 209, 1331, 2299

Step-4: Factors of 25300

List of positive integer factors of 25300 that divides 25289 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 23, 25, 44, 46, 50, 55, 92, 100, 110, 115, 220, 230, 253, 275, 460, 506, 550, 575, 1012, 1100, 1150, 1265, 2300, 2530, 5060, 6325, 12650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25289 and 25300. The biggest common factor number is the GCF number.
So the greatest common factor 25289 and 25300 is 11.

Also check out the Least Common Multiple of 25289 and 25300