What is the Greatest Common Factor of 38190 and 38209?

Greatest common factor (GCF) of 38190 and 38209 is 19.

GCF(38190,38209) = 19

We will now calculate the prime factors of 38190 and 38209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38190 and 38209.

How to find the GCF of 38190 and 38209?

We will first find the prime factorization of 38190 and 38209. After we will calculate the factors of 38190 and 38209 and find the biggest common factor number .

Step-1: Prime Factorization of 38190

Prime factors of 38190 are 2, 3, 5, 19, 67. Prime factorization of 38190 in exponential form is:

38190 = 2¹ × 3¹ × 5¹ × 19¹ × 67¹

Step-2: Prime Factorization of 38209

Prime factors of 38209 are 19, 2011. Prime factorization of 38209 in exponential form is:

38209 = 19¹ × 2011¹

Step-3: Factors of 38190

List of positive integer factors of 38190 that divides 38190 without a remainder.

1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 67, 95, 114, 134, 190, 201, 285, 335, 402, 570, 670, 1005, 1273, 2010, 2546, 3819, 6365, 7638, 12730, 19095

Step-4: Factors of 38209

List of positive integer factors of 38209 that divides 38190 without a remainder.

1, 19, 2011

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38190 and 38209. The biggest common factor number is the GCF number.
So the greatest common factor 38190 and 38209 is 19.

Also check out the Least Common Multiple of 38190 and 38209