What is the Greatest Common Factor of 3000 and 3014?

Greatest common factor (GCF) of 3000 and 3014 is 2.

GCF(3000,3014) = 2

We will now calculate the prime factors of 3000 and 3014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3000 and 3014.

How to find the GCF of 3000 and 3014?

We will first find the prime factorization of 3000 and 3014. After we will calculate the factors of 3000 and 3014 and find the biggest common factor number .

Step-1: Prime Factorization of 3000

Prime factors of 3000 are 2, 3, 5. Prime factorization of 3000 in exponential form is:

3000 = 2³ × 3¹ × 5³

Step-2: Prime Factorization of 3014

Prime factors of 3014 are 2, 11, 137. Prime factorization of 3014 in exponential form is:

3014 = 2¹ × 11¹ × 137¹

Step-3: Factors of 3000

List of positive integer factors of 3000 that divides 3000 without a remainder.

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

Step-4: Factors of 3014

List of positive integer factors of 3014 that divides 3000 without a remainder.

1, 2, 11, 22, 137, 274, 1507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3000 and 3014. The biggest common factor number is the GCF number.
So the greatest common factor 3000 and 3014 is 2.

Also check out the Least Common Multiple of 3000 and 3014