What is the Greatest Common Factor of 14257 and 14274?

Greatest common factor (GCF) of 14257 and 14274 is 1.

GCF(14257,14274) = 1

We will now calculate the prime factors of 14257 and 14274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14257 and 14274.

How to find the GCF of 14257 and 14274?

We will first find the prime factorization of 14257 and 14274. After we will calculate the factors of 14257 and 14274 and find the biggest common factor number .

Step-1: Prime Factorization of 14257

Prime factors of 14257 are 53, 269. Prime factorization of 14257 in exponential form is:

14257 = 53¹ × 269¹

Step-2: 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-3: Factors of 14257

List of positive integer factors of 14257 that divides 14257 without a remainder.

1, 53, 269

Step-4: Factors of 14274

List of positive integer factors of 14274 that divides 14257 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14257 and 14274. The biggest common factor number is the GCF number.
So the greatest common factor 14257 and 14274 is 1.

Also check out the Least Common Multiple of 14257 and 14274