What is the Greatest Common Factor of 22800 and 22809?

Greatest common factor (GCF) of 22800 and 22809 is 3.

GCF(22800,22809) = 3

We will now calculate the prime factors of 22800 and 22809, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22800 and 22809.

How to find the GCF of 22800 and 22809?

We will first find the prime factorization of 22800 and 22809. After we will calculate the factors of 22800 and 22809 and find the biggest common factor number .

Step-1: Prime Factorization of 22800

Prime factors of 22800 are 2, 3, 5, 19. Prime factorization of 22800 in exponential form is:

22800 = 2⁴ × 3¹ × 5² × 19¹

Step-2: Prime Factorization of 22809

Prime factors of 22809 are 3, 7603. Prime factorization of 22809 in exponential form is:

22809 = 3¹ × 7603¹

Step-3: Factors of 22800

List of positive integer factors of 22800 that divides 22800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 25, 30, 38, 40, 48, 50, 57, 60, 75, 76, 80, 95, 100, 114, 120, 150, 152, 190, 200, 228, 240, 285, 300, 304, 380, 400, 456, 475, 570, 600, 760, 912, 950, 1140, 1200, 1425, 1520, 1900, 2280, 2850, 3800, 4560, 5700, 7600, 11400

Step-4: Factors of 22809

List of positive integer factors of 22809 that divides 22800 without a remainder.

1, 3, 7603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22800 and 22809. The biggest common factor number is the GCF number.
So the greatest common factor 22800 and 22809 is 3.

Also check out the Least Common Multiple of 22800 and 22809