What is the Greatest Common Factor of 14508 and 14514?

Greatest common factor (GCF) of 14508 and 14514 is 6.

GCF(14508,14514) = 6

We will now calculate the prime factors of 14508 and 14514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14508 and 14514.

How to find the GCF of 14508 and 14514?

We will first find the prime factorization of 14508 and 14514. After we will calculate the factors of 14508 and 14514 and find the biggest common factor number .

Step-1: Prime Factorization of 14508

Prime factors of 14508 are 2, 3, 13, 31. Prime factorization of 14508 in exponential form is:

14508 = 2² × 3² × 13¹ × 31¹

Step-2: Prime Factorization of 14514

Prime factors of 14514 are 2, 3, 41, 59. Prime factorization of 14514 in exponential form is:

14514 = 2¹ × 3¹ × 41¹ × 59¹

Step-3: Factors of 14508

List of positive integer factors of 14508 that divides 14508 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 31, 36, 39, 52, 62, 78, 93, 117, 124, 156, 186, 234, 279, 372, 403, 468, 558, 806, 1116, 1209, 1612, 2418, 3627, 4836, 7254

Step-4: Factors of 14514

List of positive integer factors of 14514 that divides 14508 without a remainder.

1, 2, 3, 6, 41, 59, 82, 118, 123, 177, 246, 354, 2419, 4838, 7257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14508 and 14514. The biggest common factor number is the GCF number.
So the greatest common factor 14508 and 14514 is 6.

Also check out the Least Common Multiple of 14508 and 14514