What is the Greatest Common Factor of 10000 and 10014?

Greatest common factor (GCF) of 10000 and 10014 is 2.

GCF(10000,10014) = 2

We will now calculate the prime factors of 10000 and 10014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10000 and 10014.

How to find the GCF of 10000 and 10014?

We will first find the prime factorization of 10000 and 10014. After we will calculate the factors of 10000 and 10014 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 10014

Prime factors of 10014 are 2, 3, 1669. Prime factorization of 10014 in exponential form is:

10014 = 2¹ × 3¹ × 1669¹

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 10014

List of positive integer factors of 10014 that divides 10000 without a remainder.

1, 2, 3, 6, 1669, 3338, 5007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10000 and 10014. The biggest common factor number is the GCF number.
So the greatest common factor 10000 and 10014 is 2.

Also check out the Least Common Multiple of 10000 and 10014