What is the Greatest Common Factor of 6000 and 6014?

Greatest common factor (GCF) of 6000 and 6014 is 2.

GCF(6000,6014) = 2

We will now calculate the prime factors of 6000 and 6014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6000 and 6014.

How to find the GCF of 6000 and 6014?

We will first find the prime factorization of 6000 and 6014. After we will calculate the factors of 6000 and 6014 and find the biggest common factor number .

Step-1: Prime Factorization of 6000

Prime factors of 6000 are 2, 3, 5. Prime factorization of 6000 in exponential form is:

6000 = 2⁴ × 3¹ × 5³

Step-2: Prime Factorization of 6014

Prime factors of 6014 are 2, 31, 97. Prime factorization of 6014 in exponential form is:

6014 = 2¹ × 31¹ × 97¹

Step-3: Factors of 6000

List of positive integer factors of 6000 that divides 6000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000

Step-4: Factors of 6014

List of positive integer factors of 6014 that divides 6000 without a remainder.

1, 2, 31, 62, 97, 194, 3007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6000 and 6014. The biggest common factor number is the GCF number.
So the greatest common factor 6000 and 6014 is 2.

Also check out the Least Common Multiple of 6000 and 6014