What is the Greatest Common Factor of 14229 and 14238?

Greatest common factor (GCF) of 14229 and 14238 is 9.

GCF(14229,14238) = 9

We will now calculate the prime factors of 14229 and 14238, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14229 and 14238.

How to find the GCF of 14229 and 14238?

We will first find the prime factorization of 14229 and 14238. After we will calculate the factors of 14229 and 14238 and find the biggest common factor number .

Step-1: Prime Factorization of 14229

Prime factors of 14229 are 3, 17, 31. Prime factorization of 14229 in exponential form is:

14229 = 3³ × 17¹ × 31¹

Step-2: 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-3: Factors of 14229

List of positive integer factors of 14229 that divides 14229 without a remainder.

1, 3, 9, 17, 27, 31, 51, 93, 153, 279, 459, 527, 837, 1581, 4743

Step-4: Factors of 14238

List of positive integer factors of 14238 that divides 14229 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14229 and 14238. The biggest common factor number is the GCF number.
So the greatest common factor 14229 and 14238 is 9.

Also check out the Least Common Multiple of 14229 and 14238