What is the Greatest Common Factor of 3000 and 3012?

Greatest common factor (GCF) of 3000 and 3012 is 12.

GCF(3000,3012) = 12

We will now calculate the prime factors of 3000 and 3012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3000 and 3012.

How to find the GCF of 3000 and 3012?

We will first find the prime factorization of 3000 and 3012. After we will calculate the factors of 3000 and 3012 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 3012

Prime factors of 3012 are 2, 3, 251. Prime factorization of 3012 in exponential form is:

3012 = 2² × 3¹ × 251¹

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 3012

List of positive integer factors of 3012 that divides 3000 without a remainder.

1, 2, 3, 4, 6, 12, 251, 502, 753, 1004, 1506

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3000 and 3012. The biggest common factor number is the GCF number.
So the greatest common factor 3000 and 3012 is 12.

Also check out the Least Common Multiple of 3000 and 3012