What is the Greatest Common Factor of 38200 and 38205?

Greatest common factor (GCF) of 38200 and 38205 is 5.

GCF(38200,38205) = 5

We will now calculate the prime factors of 38200 and 38205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38200 and 38205.

How to find the GCF of 38200 and 38205?

We will first find the prime factorization of 38200 and 38205. After we will calculate the factors of 38200 and 38205 and find the biggest common factor number .

Step-1: Prime Factorization of 38200

Prime factors of 38200 are 2, 5, 191. Prime factorization of 38200 in exponential form is:

38200 = 2³ × 5² × 191¹

Step-2: 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-3: Factors of 38200

List of positive integer factors of 38200 that divides 38200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 191, 200, 382, 764, 955, 1528, 1910, 3820, 4775, 7640, 9550, 19100

Step-4: Factors of 38205

List of positive integer factors of 38205 that divides 38200 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38200 and 38205. The biggest common factor number is the GCF number.
So the greatest common factor 38200 and 38205 is 5.

Also check out the Least Common Multiple of 38200 and 38205