What is the Greatest Common Factor of 21209 and 21216?

Greatest common factor (GCF) of 21209 and 21216 is 1.

GCF(21209,21216) = 1

We will now calculate the prime factors of 21209 and 21216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21209 and 21216.

How to find the GCF of 21209 and 21216?

We will first find the prime factorization of 21209 and 21216. After we will calculate the factors of 21209 and 21216 and find the biggest common factor number .

Step-1: Prime Factorization of 21209

Prime factors of 21209 are 127, 167. Prime factorization of 21209 in exponential form is:

21209 = 127¹ × 167¹

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 21209

List of positive integer factors of 21209 that divides 21209 without a remainder.

1, 127, 167

Step-4: Factors of 21216

List of positive integer factors of 21216 that divides 21209 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 21209 and 21216. The biggest common factor number is the GCF number.
So the greatest common factor 21209 and 21216 is 1.

Also check out the Least Common Multiple of 21209 and 21216