What is the Greatest Common Factor of 14308 and 14314?

Greatest common factor (GCF) of 14308 and 14314 is 2.

GCF(14308,14314) = 2

We will now calculate the prime factors of 14308 and 14314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14308 and 14314.

How to find the GCF of 14308 and 14314?

We will first find the prime factorization of 14308 and 14314. After we will calculate the factors of 14308 and 14314 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 14314

Prime factors of 14314 are 2, 17, 421. Prime factorization of 14314 in exponential form is:

14314 = 2¹ × 17¹ × 421¹

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 14314

List of positive integer factors of 14314 that divides 14308 without a remainder.

1, 2, 17, 34, 421, 842, 7157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14308 and 14314. The biggest common factor number is the GCF number.
So the greatest common factor 14308 and 14314 is 2.

Also check out the Least Common Multiple of 14308 and 14314