What is the Greatest Common Factor of 21200 and 21217?

Greatest common factor (GCF) of 21200 and 21217 is 1.

GCF(21200,21217) = 1

We will now calculate the prime factors of 21200 and 21217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21200 and 21217.

How to find the GCF of 21200 and 21217?

We will first find the prime factorization of 21200 and 21217. After we will calculate the factors of 21200 and 21217 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 21217

Prime factors of 21217 are 7, 433. Prime factorization of 21217 in exponential form is:

21217 = 7² × 433¹

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 21217

List of positive integer factors of 21217 that divides 21200 without a remainder.

1, 7, 49, 433, 3031

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21200 and 21217. The biggest common factor number is the GCF number.
So the greatest common factor 21200 and 21217 is 1.

Also check out the Least Common Multiple of 21200 and 21217