What is the Greatest Common Factor of 10000 and 10007?

Greatest common factor (GCF) of 10000 and 10007 is 1.

GCF(10000,10007) = 1

We will now calculate the prime factors of 10000 and 10007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10000 and 10007.

How to find the GCF of 10000 and 10007?

We will first find the prime factorization of 10000 and 10007. After we will calculate the factors of 10000 and 10007 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 10007

Prime factors of 10007 are 10007. Prime factorization of 10007 in exponential form is:

10007 = 10007¹

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 10007

List of positive integer factors of 10007 that divides 10000 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10000 and 10007. The biggest common factor number is the GCF number.
So the greatest common factor 10000 and 10007 is 1.

Also check out the Least Common Multiple of 10000 and 10007