What is the Greatest Common Factor of 14274 and 14289?

Greatest common factor (GCF) of 14274 and 14289 is 3.

GCF(14274,14289) = 3

We will now calculate the prime factors of 14274 and 14289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14274 and 14289.

How to find the GCF of 14274 and 14289?

We will first find the prime factorization of 14274 and 14289. After we will calculate the factors of 14274 and 14289 and find the biggest common factor number .

Step-1: Prime Factorization of 14274

Prime factors of 14274 are 2, 3, 13, 61. Prime factorization of 14274 in exponential form is:

14274 = 2¹ × 3² × 13¹ × 61¹

Step-2: Prime Factorization of 14289

Prime factors of 14289 are 3, 11, 433. Prime factorization of 14289 in exponential form is:

14289 = 3¹ × 11¹ × 433¹

Step-3: Factors of 14274

List of positive integer factors of 14274 that divides 14274 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 61, 78, 117, 122, 183, 234, 366, 549, 793, 1098, 1586, 2379, 4758, 7137

Step-4: Factors of 14289

List of positive integer factors of 14289 that divides 14274 without a remainder.

1, 3, 11, 33, 433, 1299, 4763

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14274 and 14289. The biggest common factor number is the GCF number.
So the greatest common factor 14274 and 14289 is 3.

Also check out the Least Common Multiple of 14274 and 14289