What is the Greatest Common Factor of 990 and 1000?

Greatest common factor (GCF) of 990 and 1000 is 10.

GCF(990,1000) = 10

We will now calculate the prime factors of 990 and 1000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 990 and 1000.

How to find the GCF of 990 and 1000?

We will first find the prime factorization of 990 and 1000. After we will calculate the factors of 990 and 1000 and find the biggest common factor number .

Step-1: Prime Factorization of 990

Prime factors of 990 are 2, 3, 5, 11. Prime factorization of 990 in exponential form is:

990 = 2¹ × 3² × 5¹ × 11¹

Step-2: Prime Factorization of 1000

Prime factors of 1000 are 2, 5. Prime factorization of 1000 in exponential form is:

1000 = 2³ × 5³

Step-3: Factors of 990

List of positive integer factors of 990 that divides 990 without a remainder.

1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495

Step-4: Factors of 1000

List of positive integer factors of 1000 that divides 990 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 990 and 1000. The biggest common factor number is the GCF number.
So the greatest common factor 990 and 1000 is 10.

Also check out the Least Common Multiple of 990 and 1000