What is the Greatest Common Factor of 2990 and 3000?

Greatest common factor (GCF) of 2990 and 3000 is 10.

GCF(2990,3000) = 10

We will now calculate the prime factors of 2990 and 3000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2990 and 3000.

How to find the GCF of 2990 and 3000?

We will first find the prime factorization of 2990 and 3000. After we will calculate the factors of 2990 and 3000 and find the biggest common factor number .

Step-1: Prime Factorization of 2990

Prime factors of 2990 are 2, 5, 13, 23. Prime factorization of 2990 in exponential form is:

2990 = 2¹ × 5¹ × 13¹ × 23¹

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 2990

List of positive integer factors of 2990 that divides 2990 without a remainder.

1, 2, 5, 10, 13, 23, 26, 46, 65, 115, 130, 230, 299, 598, 1495

Step-4: Factors of 3000

List of positive integer factors of 3000 that divides 2990 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 2990 and 3000. The biggest common factor number is the GCF number.
So the greatest common factor 2990 and 3000 is 10.

Also check out the Least Common Multiple of 2990 and 3000