What is the Greatest Common Factor of 21204 and 21214?

Greatest common factor (GCF) of 21204 and 21214 is 2.

GCF(21204,21214) = 2

We will now calculate the prime factors of 21204 and 21214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21204 and 21214.

How to find the GCF of 21204 and 21214?

We will first find the prime factorization of 21204 and 21214. After we will calculate the factors of 21204 and 21214 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21214

Prime factors of 21214 are 2, 10607. Prime factorization of 21214 in exponential form is:

21214 = 2¹ × 10607¹

Step-3: Factors of 21204

List of positive integer factors of 21204 that divides 21204 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

Step-4: Factors of 21214

List of positive integer factors of 21214 that divides 21204 without a remainder.

1, 2, 10607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21204 and 21214. The biggest common factor number is the GCF number.
So the greatest common factor 21204 and 21214 is 2.

Also check out the Least Common Multiple of 21204 and 21214