What is the Greatest Common Factor of 21200 and 21205?

Greatest common factor (GCF) of 21200 and 21205 is 5.

GCF(21200,21205) = 5

We will now calculate the prime factors of 21200 and 21205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21200 and 21205.

How to find the GCF of 21200 and 21205?

We will first find the prime factorization of 21200 and 21205. After we will calculate the factors of 21200 and 21205 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 21205

Prime factors of 21205 are 5, 4241. Prime factorization of 21205 in exponential form is:

21205 = 5¹ × 4241¹

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 21205

List of positive integer factors of 21205 that divides 21200 without a remainder.

1, 5, 4241

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21200 and 21205. The biggest common factor number is the GCF number.
So the greatest common factor 21200 and 21205 is 5.

Also check out the Least Common Multiple of 21200 and 21205