What is the Greatest Common Factor of 5000 and 5014?

Greatest common factor (GCF) of 5000 and 5014 is 2.

GCF(5000,5014) = 2

We will now calculate the prime factors of 5000 and 5014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5000 and 5014.

How to find the GCF of 5000 and 5014?

We will first find the prime factorization of 5000 and 5014. After we will calculate the factors of 5000 and 5014 and find the biggest common factor number .

Step-1: Prime Factorization of 5000

Prime factors of 5000 are 2, 5. Prime factorization of 5000 in exponential form is:

5000 = 2³ × 5⁴

Step-2: Prime Factorization of 5014

Prime factors of 5014 are 2, 23, 109. Prime factorization of 5014 in exponential form is:

5014 = 2¹ × 23¹ × 109¹

Step-3: Factors of 5000

List of positive integer factors of 5000 that divides 5000 without a remainder.

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

Step-4: Factors of 5014

List of positive integer factors of 5014 that divides 5000 without a remainder.

1, 2, 23, 46, 109, 218, 2507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5000 and 5014. The biggest common factor number is the GCF number.
So the greatest common factor 5000 and 5014 is 2.

Also check out the Least Common Multiple of 5000 and 5014