What is the Greatest Common Factor of 38208 and 38217?

Greatest common factor (GCF) of 38208 and 38217 is 3.

GCF(38208,38217) = 3

We will now calculate the prime factors of 38208 and 38217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38208 and 38217.

How to find the GCF of 38208 and 38217?

We will first find the prime factorization of 38208 and 38217. After we will calculate the factors of 38208 and 38217 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 38217

Prime factors of 38217 are 3, 12739. Prime factorization of 38217 in exponential form is:

38217 = 3¹ × 12739¹

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 38217

List of positive integer factors of 38217 that divides 38208 without a remainder.

1, 3, 12739

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38208 and 38217. The biggest common factor number is the GCF number.
So the greatest common factor 38208 and 38217 is 3.

Also check out the Least Common Multiple of 38208 and 38217