What is the Greatest Common Factor of 21204 and 21219?

Greatest common factor (GCF) of 21204 and 21219 is 3.

GCF(21204,21219) = 3

We will now calculate the prime factors of 21204 and 21219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21204 and 21219.

How to find the GCF of 21204 and 21219?

We will first find the prime factorization of 21204 and 21219. After we will calculate the factors of 21204 and 21219 and find the biggest common factor number .

Step-1: Prime Factorization of 21204

Prime factors of 21204 are 2, 3, 19, 31. Prime factorization of 21204 in exponential form is:

21204 = 2² × 3² × 19¹ × 31¹

Step-2: Prime Factorization of 21219

Prime factors of 21219 are 3, 11, 643. Prime factorization of 21219 in exponential form is:

21219 = 3¹ × 11¹ × 643¹

Step-3: Factors of 21204

List of positive integer factors of 21204 that divides 21204 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 31, 36, 38, 57, 62, 76, 93, 114, 124, 171, 186, 228, 279, 342, 372, 558, 589, 684, 1116, 1178, 1767, 2356, 3534, 5301, 7068, 10602

Step-4: Factors of 21219

List of positive integer factors of 21219 that divides 21204 without a remainder.

1, 3, 11, 33, 643, 1929, 7073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21204 and 21219. The biggest common factor number is the GCF number.
So the greatest common factor 21204 and 21219 is 3.

Also check out the Least Common Multiple of 21204 and 21219