What is the Greatest Common Factor of 14238 and 14257?

Greatest common factor (GCF) of 14238 and 14257 is 1.

GCF(14238,14257) = 1

We will now calculate the prime factors of 14238 and 14257, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14238 and 14257.

How to find the GCF of 14238 and 14257?

We will first find the prime factorization of 14238 and 14257. After we will calculate the factors of 14238 and 14257 and find the biggest common factor number .

Step-1: Prime Factorization of 14238

Prime factors of 14238 are 2, 3, 7, 113. Prime factorization of 14238 in exponential form is:

14238 = 2¹ × 3² × 7¹ × 113¹

Step-2: Prime Factorization of 14257

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

14257 = 53¹ × 269¹

Step-3: Factors of 14238

List of positive integer factors of 14238 that divides 14238 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 113, 126, 226, 339, 678, 791, 1017, 1582, 2034, 2373, 4746, 7119

Step-4: Factors of 14257

List of positive integer factors of 14257 that divides 14238 without a remainder.

1, 53, 269

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14238 and 14257. The biggest common factor number is the GCF number.
So the greatest common factor 14238 and 14257 is 1.

Also check out the Least Common Multiple of 14238 and 14257