What is the Greatest Common Factor of 20204 and 20208?

Greatest common factor (GCF) of 20204 and 20208 is 4.

GCF(20204,20208) = 4

We will now calculate the prime factors of 20204 and 20208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20204 and 20208.

How to find the GCF of 20204 and 20208?

We will first find the prime factorization of 20204 and 20208. After we will calculate the factors of 20204 and 20208 and find the biggest common factor number .

Step-1: Prime Factorization of 20204

Prime factors of 20204 are 2, 5051. Prime factorization of 20204 in exponential form is:

20204 = 2² × 5051¹

Step-2: Prime Factorization of 20208

Prime factors of 20208 are 2, 3, 421. Prime factorization of 20208 in exponential form is:

20208 = 2⁴ × 3¹ × 421¹

Step-3: Factors of 20204

List of positive integer factors of 20204 that divides 20204 without a remainder.

1, 2, 4, 5051, 10102

Step-4: Factors of 20208

List of positive integer factors of 20208 that divides 20204 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 421, 842, 1263, 1684, 2526, 3368, 5052, 6736, 10104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20204 and 20208. The biggest common factor number is the GCF number.
So the greatest common factor 20204 and 20208 is 4.

Also check out the Least Common Multiple of 20204 and 20208