What is the Greatest Common Factor of 14308 and 14322?

Greatest common factor (GCF) of 14308 and 14322 is 14.

GCF(14308,14322) = 14

We will now calculate the prime factors of 14308 and 14322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14308 and 14322.

How to find the GCF of 14308 and 14322?

We will first find the prime factorization of 14308 and 14322. After we will calculate the factors of 14308 and 14322 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 14322

Prime factors of 14322 are 2, 3, 7, 11, 31. Prime factorization of 14322 in exponential form is:

14322 = 2¹ × 3¹ × 7¹ × 11¹ × 31¹

Step-3: Factors of 14308

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

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

Step-4: Factors of 14322

List of positive integer factors of 14322 that divides 14308 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 31, 33, 42, 62, 66, 77, 93, 154, 186, 217, 231, 341, 434, 462, 651, 682, 1023, 1302, 2046, 2387, 4774, 7161

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14308 and 14322. The biggest common factor number is the GCF number.
So the greatest common factor 14308 and 14322 is 14.

Also check out the Least Common Multiple of 14308 and 14322