What is the Greatest Common Factor of 21200 and 21204?

Greatest common factor (GCF) of 21200 and 21204 is 4.

GCF(21200,21204) = 4

We will now calculate the prime factors of 21200 and 21204, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21200 and 21204.

How to find the GCF of 21200 and 21204?

We will first find the prime factorization of 21200 and 21204. After we will calculate the factors of 21200 and 21204 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 21204

Prime factors of 21204 are 2, 3, 19, 31. Prime factorization of 21204 in exponential form is:

21204 = 2² × 3² × 19¹ × 31¹

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 21204

List of positive integer factors of 21204 that divides 21200 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 31, 36, 38, 57, 62, 76, 93, 114, 124, 171, 186, 228, 279, 342, 372, 558, 589, 684, 1116, 1178, 1767, 2356, 3534, 5301, 7068, 10602

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21200 and 21204. The biggest common factor number is the GCF number.
So the greatest common factor 21200 and 21204 is 4.

Also check out the Least Common Multiple of 21200 and 21204