What is the Greatest Common Factor of 30208 and 30224?

Greatest common factor (GCF) of 30208 and 30224 is 16.

GCF(30208,30224) = 16

We will now calculate the prime factors of 30208 and 30224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30208 and 30224.

How to find the GCF of 30208 and 30224?

We will first find the prime factorization of 30208 and 30224. After we will calculate the factors of 30208 and 30224 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 30224

Prime factors of 30224 are 2, 1889. Prime factorization of 30224 in exponential form is:

30224 = 2⁴ × 1889¹

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 30224

List of positive integer factors of 30224 that divides 30208 without a remainder.

1, 2, 4, 8, 16, 1889, 3778, 7556, 15112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30208 and 30224. The biggest common factor number is the GCF number.
So the greatest common factor 30208 and 30224 is 16.

Also check out the Least Common Multiple of 30208 and 30224