What is the Greatest Common Factor of 1990 and 2000?

Greatest common factor (GCF) of 1990 and 2000 is 10.

GCF(1990,2000) = 10

We will now calculate the prime factors of 1990 and 2000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1990 and 2000.

How to find the GCF of 1990 and 2000?

We will first find the prime factorization of 1990 and 2000. After we will calculate the factors of 1990 and 2000 and find the biggest common factor number .

Step-1: Prime Factorization of 1990

Prime factors of 1990 are 2, 5, 199. Prime factorization of 1990 in exponential form is:

1990 = 2¹ × 5¹ × 199¹

Step-2: Prime Factorization of 2000

Prime factors of 2000 are 2, 5. Prime factorization of 2000 in exponential form is:

2000 = 2⁴ × 5³

Step-3: Factors of 1990

List of positive integer factors of 1990 that divides 1990 without a remainder.

1, 2, 5, 10, 199, 398, 995

Step-4: Factors of 2000

List of positive integer factors of 2000 that divides 1990 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1990 and 2000. The biggest common factor number is the GCF number.
So the greatest common factor 1990 and 2000 is 10.

Also check out the Least Common Multiple of 1990 and 2000