What is the Greatest Common Factor of 25000 and 25009?

Greatest common factor (GCF) of 25000 and 25009 is 1.

GCF(25000,25009) = 1

We will now calculate the prime factors of 25000 and 25009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25000 and 25009.

How to find the GCF of 25000 and 25009?

We will first find the prime factorization of 25000 and 25009. After we will calculate the factors of 25000 and 25009 and find the biggest common factor number .

Step-1: Prime Factorization of 25000

Prime factors of 25000 are 2, 5. Prime factorization of 25000 in exponential form is:

25000 = 2³ × 5⁵

Step-2: Prime Factorization of 25009

Prime factors of 25009 are 89, 281. Prime factorization of 25009 in exponential form is:

25009 = 89¹ × 281¹

Step-3: Factors of 25000

List of positive integer factors of 25000 that divides 25000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 3125, 5000, 6250, 12500

Step-4: Factors of 25009

List of positive integer factors of 25009 that divides 25000 without a remainder.

1, 89, 281

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25000 and 25009. The biggest common factor number is the GCF number.
So the greatest common factor 25000 and 25009 is 1.

Also check out the Least Common Multiple of 25000 and 25009