What is the Greatest Common Factor of 14304 and 14308?

Greatest common factor (GCF) of 14304 and 14308 is 4.

GCF(14304,14308) = 4

We will now calculate the prime factors of 14304 and 14308, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14304 and 14308.

How to find the GCF of 14304 and 14308?

We will first find the prime factorization of 14304 and 14308. After we will calculate the factors of 14304 and 14308 and find the biggest common factor number .

Step-1: Prime Factorization of 14304

Prime factors of 14304 are 2, 3, 149. Prime factorization of 14304 in exponential form is:

14304 = 2⁵ × 3¹ × 149¹

Step-2: Prime Factorization of 14308

Prime factors of 14308 are 2, 7, 73. Prime factorization of 14308 in exponential form is:

14308 = 2² × 7² × 73¹

Step-3: Factors of 14304

List of positive integer factors of 14304 that divides 14304 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 149, 298, 447, 596, 894, 1192, 1788, 2384, 3576, 4768, 7152

Step-4: Factors of 14308

List of positive integer factors of 14308 that divides 14304 without a remainder.

1, 2, 4, 7, 14, 28, 49, 73, 98, 146, 196, 292, 511, 1022, 2044, 3577, 7154

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14304 and 14308. The biggest common factor number is the GCF number.
So the greatest common factor 14304 and 14308 is 4.

Also check out the Least Common Multiple of 14304 and 14308