What is the Greatest Common Factor of 23000 and 23009?

Greatest common factor (GCF) of 23000 and 23009 is 1.

GCF(23000,23009) = 1

We will now calculate the prime factors of 23000 and 23009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23000 and 23009.

How to find the GCF of 23000 and 23009?

We will first find the prime factorization of 23000 and 23009. After we will calculate the factors of 23000 and 23009 and find the biggest common factor number .

Step-1: Prime Factorization of 23000

Prime factors of 23000 are 2, 5, 23. Prime factorization of 23000 in exponential form is:

23000 = 2³ × 5³ × 23¹

Step-2: Prime Factorization of 23009

Prime factors of 23009 are 7, 19, 173. Prime factorization of 23009 in exponential form is:

23009 = 7¹ × 19¹ × 173¹

Step-3: Factors of 23000

List of positive integer factors of 23000 that divides 23000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 23, 25, 40, 46, 50, 92, 100, 115, 125, 184, 200, 230, 250, 460, 500, 575, 920, 1000, 1150, 2300, 2875, 4600, 5750, 11500

Step-4: Factors of 23009

List of positive integer factors of 23009 that divides 23000 without a remainder.

1, 7, 19, 133, 173, 1211, 3287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23000 and 23009. The biggest common factor number is the GCF number.
So the greatest common factor 23000 and 23009 is 1.

Also check out the Least Common Multiple of 23000 and 23009