What is the Greatest Common Factor of 1000 and 1009?

Greatest common factor (GCF) of 1000 and 1009 is 1.

GCF(1000,1009) = 1

We will now calculate the prime factors of 1000 and 1009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1000 and 1009.

How to find the GCF of 1000 and 1009?

We will first find the prime factorization of 1000 and 1009. After we will calculate the factors of 1000 and 1009 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 1009

Prime factors of 1009 are 1009. Prime factorization of 1009 in exponential form is:

1009 = 1009¹

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 1009

List of positive integer factors of 1009 that divides 1000 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1000 and 1009. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1009 is 1.

Also check out the Least Common Multiple of 1000 and 1009