What is the Greatest Common Factor of 3000 and 3005?

Greatest common factor (GCF) of 3000 and 3005 is 5.

GCF(3000,3005) = 5

We will now calculate the prime factors of 3000 and 3005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3000 and 3005.

How to find the GCF of 3000 and 3005?

We will first find the prime factorization of 3000 and 3005. After we will calculate the factors of 3000 and 3005 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 3005

Prime factors of 3005 are 5, 601. Prime factorization of 3005 in exponential form is:

3005 = 5¹ × 601¹

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 3005

List of positive integer factors of 3005 that divides 3000 without a remainder.

1, 5, 601

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3000 and 3005. The biggest common factor number is the GCF number.
So the greatest common factor 3000 and 3005 is 5.

Also check out the Least Common Multiple of 3000 and 3005