What is the Greatest Common Factor of 38214 and 38229?

Greatest common factor (GCF) of 38214 and 38229 is 3.

GCF(38214,38229) = 3

We will now calculate the prime factors of 38214 and 38229, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38214 and 38229.

How to find the GCF of 38214 and 38229?

We will first find the prime factorization of 38214 and 38229. After we will calculate the factors of 38214 and 38229 and find the biggest common factor number .

Step-1: Prime Factorization of 38214

Prime factors of 38214 are 2, 3, 11, 193. Prime factorization of 38214 in exponential form is:

38214 = 2¹ × 3² × 11¹ × 193¹

Step-2: Prime Factorization of 38229

Prime factors of 38229 are 3, 12743. Prime factorization of 38229 in exponential form is:

38229 = 3¹ × 12743¹

Step-3: Factors of 38214

List of positive integer factors of 38214 that divides 38214 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 193, 198, 386, 579, 1158, 1737, 2123, 3474, 4246, 6369, 12738, 19107

Step-4: Factors of 38229

List of positive integer factors of 38229 that divides 38214 without a remainder.

1, 3, 12743

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38214 and 38229. The biggest common factor number is the GCF number.
So the greatest common factor 38214 and 38229 is 3.

Also check out the Least Common Multiple of 38214 and 38229