What is the Greatest Common Factor of 21812 and 21819?

Greatest common factor (GCF) of 21812 and 21819 is 7.

GCF(21812,21819) = 7

We will now calculate the prime factors of 21812 and 21819, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21812 and 21819.

How to find the GCF of 21812 and 21819?

We will first find the prime factorization of 21812 and 21819. After we will calculate the factors of 21812 and 21819 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21819

Prime factors of 21819 are 3, 7, 1039. Prime factorization of 21819 in exponential form is:

21819 = 3¹ × 7¹ × 1039¹

Step-3: Factors of 21812

List of positive integer factors of 21812 that divides 21812 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

Step-4: Factors of 21819

List of positive integer factors of 21819 that divides 21812 without a remainder.

1, 3, 7, 21, 1039, 3117, 7273

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21812 and 21819. The biggest common factor number is the GCF number.
So the greatest common factor 21812 and 21819 is 7.

Also check out the Least Common Multiple of 21812 and 21819