What is the Greatest Common Factor of 20889 and 20900?

Greatest common factor (GCF) of 20889 and 20900 is 11.

GCF(20889,20900) = 11

We will now calculate the prime factors of 20889 and 20900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20889 and 20900.

How to find the GCF of 20889 and 20900?

We will first find the prime factorization of 20889 and 20900. After we will calculate the factors of 20889 and 20900 and find the biggest common factor number .

Step-1: Prime Factorization of 20889

Prime factors of 20889 are 3, 11, 211. Prime factorization of 20889 in exponential form is:

20889 = 3² × 11¹ × 211¹

Step-2: Prime Factorization of 20900

Prime factors of 20900 are 2, 5, 11, 19. Prime factorization of 20900 in exponential form is:

20900 = 2² × 5² × 11¹ × 19¹

Step-3: Factors of 20889

List of positive integer factors of 20889 that divides 20889 without a remainder.

1, 3, 9, 11, 33, 99, 211, 633, 1899, 2321, 6963

Step-4: Factors of 20900

List of positive integer factors of 20900 that divides 20889 without a remainder.

1, 2, 4, 5, 10, 11, 19, 20, 22, 25, 38, 44, 50, 55, 76, 95, 100, 110, 190, 209, 220, 275, 380, 418, 475, 550, 836, 950, 1045, 1100, 1900, 2090, 4180, 5225, 10450

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20889 and 20900. The biggest common factor number is the GCF number.
So the greatest common factor 20889 and 20900 is 11.

Also check out the Least Common Multiple of 20889 and 20900