What is the Greatest Common Factor of 25789 and 25800?

Greatest common factor (GCF) of 25789 and 25800 is 1.

GCF(25789,25800) = 1

We will now calculate the prime factors of 25789 and 25800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25789 and 25800.

How to find the GCF of 25789 and 25800?

We will first find the prime factorization of 25789 and 25800. After we will calculate the factors of 25789 and 25800 and find the biggest common factor number .

Step-1: Prime Factorization of 25789

Prime factors of 25789 are 17, 37, 41. Prime factorization of 25789 in exponential form is:

25789 = 17¹ × 37¹ × 41¹

Step-2: 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-3: Factors of 25789

List of positive integer factors of 25789 that divides 25789 without a remainder.

1, 17, 37, 41, 629, 697, 1517

Step-4: Factors of 25800

List of positive integer factors of 25800 that divides 25789 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25789 and 25800. The biggest common factor number is the GCF number.
So the greatest common factor 25789 and 25800 is 1.

Also check out the Least Common Multiple of 25789 and 25800