What is the Greatest Common Factor of 10000 and 10013?

Greatest common factor (GCF) of 10000 and 10013 is 1.

GCF(10000,10013) = 1

We will now calculate the prime factors of 10000 and 10013, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10000 and 10013.

How to find the GCF of 10000 and 10013?

We will first find the prime factorization of 10000 and 10013. After we will calculate the factors of 10000 and 10013 and find the biggest common factor number .

Step-1: Prime Factorization of 10000

Prime factors of 10000 are 2, 5. Prime factorization of 10000 in exponential form is:

10000 = 2⁴ × 5⁴

Step-2: Prime Factorization of 10013

Prime factors of 10013 are 17, 19, 31. Prime factorization of 10013 in exponential form is:

10013 = 17¹ × 19¹ × 31¹

Step-3: Factors of 10000

List of positive integer factors of 10000 that divides 10000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000

Step-4: Factors of 10013

List of positive integer factors of 10013 that divides 10000 without a remainder.

1, 17, 19, 31, 323, 527, 589

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10000 and 10013. The biggest common factor number is the GCF number.
So the greatest common factor 10000 and 10013 is 1.

Also check out the Least Common Multiple of 10000 and 10013