What is the Greatest Common Factor of 21216 and 21225?

Greatest common factor (GCF) of 21216 and 21225 is 3.

GCF(21216,21225) = 3

We will now calculate the prime factors of 21216 and 21225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21216 and 21225.

How to find the GCF of 21216 and 21225?

We will first find the prime factorization of 21216 and 21225. After we will calculate the factors of 21216 and 21225 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21225

Prime factors of 21225 are 3, 5, 283. Prime factorization of 21225 in exponential form is:

21225 = 3¹ × 5² × 283¹

Step-3: Factors of 21216

List of positive integer factors of 21216 that divides 21216 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

Step-4: Factors of 21225

List of positive integer factors of 21225 that divides 21216 without a remainder.

1, 3, 5, 15, 25, 75, 283, 849, 1415, 4245, 7075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21216 and 21225. The biggest common factor number is the GCF number.
So the greatest common factor 21216 and 21225 is 3.

Also check out the Least Common Multiple of 21216 and 21225