What is the Greatest Common Factor of 21200 and 21216?

Greatest common factor (GCF) of 21200 and 21216 is 16.

GCF(21200,21216) = 16

We will now calculate the prime factors of 21200 and 21216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21200 and 21216.

How to find the GCF of 21200 and 21216?

We will first find the prime factorization of 21200 and 21216. After we will calculate the factors of 21200 and 21216 and find the biggest common factor number .

Step-1: Prime Factorization of 21200

Prime factors of 21200 are 2, 5, 53. Prime factorization of 21200 in exponential form is:

21200 = 2⁴ × 5² × 53¹

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 21200

List of positive integer factors of 21200 that divides 21200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 53, 80, 100, 106, 200, 212, 265, 400, 424, 530, 848, 1060, 1325, 2120, 2650, 4240, 5300, 10600

Step-4: Factors of 21216

List of positive integer factors of 21216 that divides 21200 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 21200 and 21216. The biggest common factor number is the GCF number.
So the greatest common factor 21200 and 21216 is 16.

Also check out the Least Common Multiple of 21200 and 21216