What is the Greatest Common Factor of 21204 and 21216?

Greatest common factor (GCF) of 21204 and 21216 is 12.

GCF(21204,21216) = 12

We will now calculate the prime factors of 21204 and 21216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21204 and 21216.

How to find the GCF of 21204 and 21216?

We will first find the prime factorization of 21204 and 21216. After we will calculate the factors of 21204 and 21216 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 21216

Prime factors of 21216 are 2, 3, 13, 17. Prime factorization of 21216 in exponential form is:

21216 = 2⁵ × 3¹ × 13¹ × 17¹

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 21216

List of positive integer factors of 21216 that divides 21204 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 17, 24, 26, 32, 34, 39, 48, 51, 52, 68, 78, 96, 102, 104, 136, 156, 204, 208, 221, 272, 312, 408, 416, 442, 544, 624, 663, 816, 884, 1248, 1326, 1632, 1768, 2652, 3536, 5304, 7072, 10608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21204 and 21216. The biggest common factor number is the GCF number.
So the greatest common factor 21204 and 21216 is 12.

Also check out the Least Common Multiple of 21204 and 21216