What is the Greatest Common Factor of 25800 and 25809?

Greatest common factor (GCF) of 25800 and 25809 is 3.

GCF(25800,25809) = 3

We will now calculate the prime factors of 25800 and 25809, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25800 and 25809.

How to find the GCF of 25800 and 25809?

We will first find the prime factorization of 25800 and 25809. After we will calculate the factors of 25800 and 25809 and find the biggest common factor number .

Step-1: Prime Factorization of 25800

Prime factors of 25800 are 2, 3, 5, 43. Prime factorization of 25800 in exponential form is:

25800 = 2³ × 3¹ × 5² × 43¹

Step-2: Prime Factorization of 25809

Prime factors of 25809 are 3, 7, 1229. Prime factorization of 25809 in exponential form is:

25809 = 3¹ × 7¹ × 1229¹

Step-3: Factors of 25800

List of positive integer factors of 25800 that divides 25800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 43, 50, 60, 75, 86, 100, 120, 129, 150, 172, 200, 215, 258, 300, 344, 430, 516, 600, 645, 860, 1032, 1075, 1290, 1720, 2150, 2580, 3225, 4300, 5160, 6450, 8600, 12900

Step-4: Factors of 25809

List of positive integer factors of 25809 that divides 25800 without a remainder.

1, 3, 7, 21, 1229, 3687, 8603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25800 and 25809. The biggest common factor number is the GCF number.
So the greatest common factor 25800 and 25809 is 3.

Also check out the Least Common Multiple of 25800 and 25809