What is the Greatest Common Factor of 2980 and 3000?

Greatest common factor (GCF) of 2980 and 3000 is 20.

GCF(2980,3000) = 20

We will now calculate the prime factors of 2980 and 3000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2980 and 3000.

How to find the GCF of 2980 and 3000?

We will first find the prime factorization of 2980 and 3000. After we will calculate the factors of 2980 and 3000 and find the biggest common factor number .

Step-1: Prime Factorization of 2980

Prime factors of 2980 are 2, 5, 149. Prime factorization of 2980 in exponential form is:

2980 = 2² × 5¹ × 149¹

Step-2: 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-3: Factors of 2980

List of positive integer factors of 2980 that divides 2980 without a remainder.

1, 2, 4, 5, 10, 20, 149, 298, 596, 745, 1490

Step-4: Factors of 3000

List of positive integer factors of 3000 that divides 2980 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2980 and 3000. The biggest common factor number is the GCF number.
So the greatest common factor 2980 and 3000 is 20.

Also check out the Least Common Multiple of 2980 and 3000