What is the Greatest Common Factor of 1000 and 1006?

Greatest common factor (GCF) of 1000 and 1006 is 2.

GCF(1000,1006) = 2

We will now calculate the prime factors of 1000 and 1006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1000 and 1006.

How to find the GCF of 1000 and 1006?

We will first find the prime factorization of 1000 and 1006. After we will calculate the factors of 1000 and 1006 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 1006

Prime factors of 1006 are 2, 503. Prime factorization of 1006 in exponential form is:

1006 = 2¹ × 503¹

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 1006

List of positive integer factors of 1006 that divides 1000 without a remainder.

1, 2, 503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1000 and 1006. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1006 is 2.

Also check out the Least Common Multiple of 1000 and 1006