What is the Greatest Common Factor of 30208 and 30228?

Greatest common factor (GCF) of 30208 and 30228 is 4.

GCF(30208,30228) = 4

We will now calculate the prime factors of 30208 and 30228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30208 and 30228.

How to find the GCF of 30208 and 30228?

We will first find the prime factorization of 30208 and 30228. After we will calculate the factors of 30208 and 30228 and find the biggest common factor number .

Step-1: Prime Factorization of 30208

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

30208 = 2⁹ × 59¹

Step-2: Prime Factorization of 30228

Prime factors of 30228 are 2, 3, 11, 229. Prime factorization of 30228 in exponential form is:

30228 = 2² × 3¹ × 11¹ × 229¹

Step-3: Factors of 30208

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

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

Step-4: Factors of 30228

List of positive integer factors of 30228 that divides 30208 without a remainder.

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132, 229, 458, 687, 916, 1374, 2519, 2748, 5038, 7557, 10076, 15114

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30208 and 30228. The biggest common factor number is the GCF number.
So the greatest common factor 30208 and 30228 is 4.

Also check out the Least Common Multiple of 30208 and 30228