What is the Greatest Common Factor of 21789 and 21800?

Greatest common factor (GCF) of 21789 and 21800 is 1.

GCF(21789,21800) = 1

We will now calculate the prime factors of 21789 and 21800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21789 and 21800.

How to find the GCF of 21789 and 21800?

We will first find the prime factorization of 21789 and 21800. After we will calculate the factors of 21789 and 21800 and find the biggest common factor number .

Step-1: Prime Factorization of 21789

Prime factors of 21789 are 3, 269. Prime factorization of 21789 in exponential form is:

21789 = 3⁴ × 269¹

Step-2: Prime Factorization of 21800

Prime factors of 21800 are 2, 5, 109. Prime factorization of 21800 in exponential form is:

21800 = 2³ × 5² × 109¹

Step-3: Factors of 21789

List of positive integer factors of 21789 that divides 21789 without a remainder.

1, 3, 9, 27, 81, 269, 807, 2421, 7263

Step-4: Factors of 21800

List of positive integer factors of 21800 that divides 21789 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 109, 200, 218, 436, 545, 872, 1090, 2180, 2725, 4360, 5450, 10900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21789 and 21800. The biggest common factor number is the GCF number.
So the greatest common factor 21789 and 21800 is 1.

Also check out the Least Common Multiple of 21789 and 21800