What is the Greatest Common Factor of 22789 and 22800?

Greatest common factor (GCF) of 22789 and 22800 is 1.

GCF(22789,22800) = 1

We will now calculate the prime factors of 22789 and 22800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22789 and 22800.

How to find the GCF of 22789 and 22800?

We will first find the prime factorization of 22789 and 22800. After we will calculate the factors of 22789 and 22800 and find the biggest common factor number .

Step-1: Prime Factorization of 22789

Prime factors of 22789 are 13, 1753. Prime factorization of 22789 in exponential form is:

22789 = 13¹ × 1753¹

Step-2: 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-3: Factors of 22789

List of positive integer factors of 22789 that divides 22789 without a remainder.

1, 13, 1753

Step-4: Factors of 22800

List of positive integer factors of 22800 that divides 22789 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22789 and 22800. The biggest common factor number is the GCF number.
So the greatest common factor 22789 and 22800 is 1.

Also check out the Least Common Multiple of 22789 and 22800