What is the Greatest Common Factor of 1000 and 1020?

Greatest common factor (GCF) of 1000 and 1020 is 20.

GCF(1000,1020) = 20

We will now calculate the prime factors of 1000 and 1020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1000 and 1020.

How to find the GCF of 1000 and 1020?

We will first find the prime factorization of 1000 and 1020. After we will calculate the factors of 1000 and 1020 and find the biggest common factor number .

Step-1: Prime Factorization of 1000

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

1000 = 2³ × 5³

Step-2: Prime Factorization of 1020

Prime factors of 1020 are 2, 3, 5, 17. Prime factorization of 1020 in exponential form is:

1020 = 2² × 3¹ × 5¹ × 17¹

Step-3: Factors of 1000

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

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

Step-4: Factors of 1020

List of positive integer factors of 1020 that divides 1000 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1000 and 1020. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1020 is 20.

Also check out the Least Common Multiple of 1000 and 1020