What is the Greatest Common Factor of 8204 and 8224?

Greatest common factor (GCF) of 8204 and 8224 is 4.

GCF(8204,8224) = 4

We will now calculate the prime factors of 8204 and 8224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8204 and 8224.

How to find the GCF of 8204 and 8224?

We will first find the prime factorization of 8204 and 8224. After we will calculate the factors of 8204 and 8224 and find the biggest common factor number .

Step-1: Prime Factorization of 8204

Prime factors of 8204 are 2, 7, 293. Prime factorization of 8204 in exponential form is:

8204 = 2² × 7¹ × 293¹

Step-2: Prime Factorization of 8224

Prime factors of 8224 are 2, 257. Prime factorization of 8224 in exponential form is:

8224 = 2⁵ × 257¹

Step-3: Factors of 8204

List of positive integer factors of 8204 that divides 8204 without a remainder.

1, 2, 4, 7, 14, 28, 293, 586, 1172, 2051, 4102

Step-4: Factors of 8224

List of positive integer factors of 8224 that divides 8204 without a remainder.

1, 2, 4, 8, 16, 32, 257, 514, 1028, 2056, 4112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8204 and 8224. The biggest common factor number is the GCF number.
So the greatest common factor 8204 and 8224 is 4.

Also check out the Least Common Multiple of 8204 and 8224