What is the Greatest Common Factor of 25000 and 25010?

Greatest common factor (GCF) of 25000 and 25010 is 10.

GCF(25000,25010) = 10

We will now calculate the prime factors of 25000 and 25010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25000 and 25010.

How to find the GCF of 25000 and 25010?

We will first find the prime factorization of 25000 and 25010. After we will calculate the factors of 25000 and 25010 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 25010

Prime factors of 25010 are 2, 5, 41, 61. Prime factorization of 25010 in exponential form is:

25010 = 2¹ × 5¹ × 41¹ × 61¹

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 25010

List of positive integer factors of 25010 that divides 25000 without a remainder.

1, 2, 5, 10, 41, 61, 82, 122, 205, 305, 410, 610, 2501, 5002, 12505

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25000 and 25010. The biggest common factor number is the GCF number.
So the greatest common factor 25000 and 25010 is 10.

Also check out the Least Common Multiple of 25000 and 25010