What is the Greatest Common Factor of 8204 and 8208?

Greatest common factor (GCF) of 8204 and 8208 is 4.

GCF(8204,8208) = 4

We will now calculate the prime factors of 8204 and 8208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8204 and 8208.

How to find the GCF of 8204 and 8208?

We will first find the prime factorization of 8204 and 8208. After we will calculate the factors of 8204 and 8208 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 8208

Prime factors of 8208 are 2, 3, 19. Prime factorization of 8208 in exponential form is:

8208 = 2⁴ × 3³ × 19¹

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 8208

List of positive integer factors of 8208 that divides 8204 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 36, 38, 48, 54, 57, 72, 76, 108, 114, 144, 152, 171, 216, 228, 304, 342, 432, 456, 513, 684, 912, 1026, 1368, 2052, 2736, 4104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8204 and 8208. The biggest common factor number is the GCF number.
So the greatest common factor 8204 and 8208 is 4.

Also check out the Least Common Multiple of 8204 and 8208