What is the Greatest Common Factor of 38208 and 38219?

Greatest common factor (GCF) of 38208 and 38219 is 1.

GCF(38208,38219) = 1

We will now calculate the prime factors of 38208 and 38219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38208 and 38219.

How to find the GCF of 38208 and 38219?

We will first find the prime factorization of 38208 and 38219. After we will calculate the factors of 38208 and 38219 and find the biggest common factor number .

Step-1: Prime Factorization of 38208

Prime factors of 38208 are 2, 3, 199. Prime factorization of 38208 in exponential form is:

38208 = 2⁶ × 3¹ × 199¹

Step-2: Prime Factorization of 38219

Prime factors of 38219 are 38219. Prime factorization of 38219 in exponential form is:

38219 = 38219¹

Step-3: Factors of 38208

List of positive integer factors of 38208 that divides 38208 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 199, 398, 597, 796, 1194, 1592, 2388, 3184, 4776, 6368, 9552, 12736, 19104

Step-4: Factors of 38219

List of positive integer factors of 38219 that divides 38208 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38208 and 38219. The biggest common factor number is the GCF number.
So the greatest common factor 38208 and 38219 is 1.

Also check out the Least Common Multiple of 38208 and 38219