What is the Greatest Common Factor of 21184 and 21200?

Greatest common factor (GCF) of 21184 and 21200 is 16.

GCF(21184,21200) = 16

We will now calculate the prime factors of 21184 and 21200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21184 and 21200.

How to find the GCF of 21184 and 21200?

We will first find the prime factorization of 21184 and 21200. After we will calculate the factors of 21184 and 21200 and find the biggest common factor number .

Step-1: Prime Factorization of 21184

Prime factors of 21184 are 2, 331. Prime factorization of 21184 in exponential form is:

21184 = 2⁶ × 331¹

Step-2: 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-3: Factors of 21184

List of positive integer factors of 21184 that divides 21184 without a remainder.

1, 2, 4, 8, 16, 32, 64, 331, 662, 1324, 2648, 5296, 10592

Step-4: Factors of 21200

List of positive integer factors of 21200 that divides 21184 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21184 and 21200. The biggest common factor number is the GCF number.
So the greatest common factor 21184 and 21200 is 16.

Also check out the Least Common Multiple of 21184 and 21200