What is the Greatest Common Factor of 22995 and 23000?

Greatest common factor (GCF) of 22995 and 23000 is 5.

GCF(22995,23000) = 5

We will now calculate the prime factors of 22995 and 23000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22995 and 23000.

How to find the GCF of 22995 and 23000?

We will first find the prime factorization of 22995 and 23000. After we will calculate the factors of 22995 and 23000 and find the biggest common factor number .

Step-1: Prime Factorization of 22995

Prime factors of 22995 are 3, 5, 7, 73. Prime factorization of 22995 in exponential form is:

22995 = 3² × 5¹ × 7¹ × 73¹

Step-2: 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-3: Factors of 22995

List of positive integer factors of 22995 that divides 22995 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 73, 105, 219, 315, 365, 511, 657, 1095, 1533, 2555, 3285, 4599, 7665

Step-4: Factors of 23000

List of positive integer factors of 23000 that divides 22995 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22995 and 23000. The biggest common factor number is the GCF number.
So the greatest common factor 22995 and 23000 is 5.

Also check out the Least Common Multiple of 22995 and 23000