What is the Greatest Common Factor of 3006 and 3024?

Greatest common factor (GCF) of 3006 and 3024 is 18.

GCF(3006,3024) = 18

We will now calculate the prime factors of 3006 and 3024, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3006 and 3024.

How to find the GCF of 3006 and 3024?

We will first find the prime factorization of 3006 and 3024. After we will calculate the factors of 3006 and 3024 and find the biggest common factor number .

Step-1: Prime Factorization of 3006

Prime factors of 3006 are 2, 3, 167. Prime factorization of 3006 in exponential form is:

3006 = 2¹ × 3² × 167¹

Step-2: Prime Factorization of 3024

Prime factors of 3024 are 2, 3, 7. Prime factorization of 3024 in exponential form is:

3024 = 2⁴ × 3³ × 7¹

Step-3: Factors of 3006

List of positive integer factors of 3006 that divides 3006 without a remainder.

1, 2, 3, 6, 9, 18, 167, 334, 501, 1002, 1503

Step-4: Factors of 3024

List of positive integer factors of 3024 that divides 3006 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 84, 108, 112, 126, 144, 168, 189, 216, 252, 336, 378, 432, 504, 756, 1008, 1512

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3006 and 3024. The biggest common factor number is the GCF number.
So the greatest common factor 3006 and 3024 is 18.

Also check out the Least Common Multiple of 3006 and 3024