What is the Greatest Common Factor of 21800 and 21812?

Greatest common factor (GCF) of 21800 and 21812 is 4.

GCF(21800,21812) = 4

We will now calculate the prime factors of 21800 and 21812, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21800 and 21812.

How to find the GCF of 21800 and 21812?

We will first find the prime factorization of 21800 and 21812. After we will calculate the factors of 21800 and 21812 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21812

Prime factors of 21812 are 2, 7, 19, 41. Prime factorization of 21812 in exponential form is:

21812 = 2² × 7¹ × 19¹ × 41¹

Step-3: Factors of 21800

List of positive integer factors of 21800 that divides 21800 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

Step-4: Factors of 21812

List of positive integer factors of 21812 that divides 21800 without a remainder.

1, 2, 4, 7, 14, 19, 28, 38, 41, 76, 82, 133, 164, 266, 287, 532, 574, 779, 1148, 1558, 3116, 5453, 10906

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21800 and 21812. The biggest common factor number is the GCF number.
So the greatest common factor 21800 and 21812 is 4.

Also check out the Least Common Multiple of 21800 and 21812