What is the Greatest Common Factor of 30204 and 30208?

Greatest common factor (GCF) of 30204 and 30208 is 4.

GCF(30204,30208) = 4

We will now calculate the prime factors of 30204 and 30208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30204 and 30208.

How to find the GCF of 30204 and 30208?

We will first find the prime factorization of 30204 and 30208. After we will calculate the factors of 30204 and 30208 and find the biggest common factor number .

Step-1: Prime Factorization of 30204

Prime factors of 30204 are 2, 3, 839. Prime factorization of 30204 in exponential form is:

30204 = 2² × 3² × 839¹

Step-2: Prime Factorization of 30208

Prime factors of 30208 are 2, 59. Prime factorization of 30208 in exponential form is:

30208 = 2⁹ × 59¹

Step-3: Factors of 30204

List of positive integer factors of 30204 that divides 30204 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 839, 1678, 2517, 3356, 5034, 7551, 10068, 15102

Step-4: Factors of 30208

List of positive integer factors of 30208 that divides 30204 without a remainder.

1, 2, 4, 8, 16, 32, 59, 64, 118, 128, 236, 256, 472, 512, 944, 1888, 3776, 7552, 15104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30204 and 30208. The biggest common factor number is the GCF number.
So the greatest common factor 30204 and 30208 is 4.

Also check out the Least Common Multiple of 30204 and 30208