What is the Greatest Common Factor of 11000 and 11009?

Greatest common factor (GCF) of 11000 and 11009 is 1.

GCF(11000,11009) = 1

We will now calculate the prime factors of 11000 and 11009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11000 and 11009.

How to find the GCF of 11000 and 11009?

We will first find the prime factorization of 11000 and 11009. After we will calculate the factors of 11000 and 11009 and find the biggest common factor number .

Step-1: Prime Factorization of 11000

Prime factors of 11000 are 2, 5, 11. Prime factorization of 11000 in exponential form is:

11000 = 2³ × 5³ × 11¹

Step-2: Prime Factorization of 11009

Prime factors of 11009 are 101, 109. Prime factorization of 11009 in exponential form is:

11009 = 101¹ × 109¹

Step-3: Factors of 11000

List of positive integer factors of 11000 that divides 11000 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 125, 200, 220, 250, 275, 440, 500, 550, 1000, 1100, 1375, 2200, 2750, 5500

Step-4: Factors of 11009

List of positive integer factors of 11009 that divides 11000 without a remainder.

1, 101, 109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11000 and 11009. The biggest common factor number is the GCF number.
So the greatest common factor 11000 and 11009 is 1.

Also check out the Least Common Multiple of 11000 and 11009