What is the Greatest Common Factor of 38205 and 38223?

Greatest common factor (GCF) of 38205 and 38223 is 9.

GCF(38205,38223) = 9

We will now calculate the prime factors of 38205 and 38223, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38205 and 38223.

How to find the GCF of 38205 and 38223?

We will first find the prime factorization of 38205 and 38223. After we will calculate the factors of 38205 and 38223 and find the biggest common factor number .

Step-1: Prime Factorization of 38205

Prime factors of 38205 are 3, 5, 283. Prime factorization of 38205 in exponential form is:

38205 = 3³ × 5¹ × 283¹

Step-2: Prime Factorization of 38223

Prime factors of 38223 are 3, 31, 137. Prime factorization of 38223 in exponential form is:

38223 = 3² × 31¹ × 137¹

Step-3: Factors of 38205

List of positive integer factors of 38205 that divides 38205 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 283, 849, 1415, 2547, 4245, 7641, 12735

Step-4: Factors of 38223

List of positive integer factors of 38223 that divides 38205 without a remainder.

1, 3, 9, 31, 93, 137, 279, 411, 1233, 4247, 12741

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38205 and 38223. The biggest common factor number is the GCF number.
So the greatest common factor 38205 and 38223 is 9.

Also check out the Least Common Multiple of 38205 and 38223