What is the Greatest Common Factor of 38198 and 38208?

Greatest common factor (GCF) of 38198 and 38208 is 2.

GCF(38198,38208) = 2

We will now calculate the prime factors of 38198 and 38208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38198 and 38208.

How to find the GCF of 38198 and 38208?

We will first find the prime factorization of 38198 and 38208. After we will calculate the factors of 38198 and 38208 and find the biggest common factor number .

Step-1: Prime Factorization of 38198

Prime factors of 38198 are 2, 71, 269. Prime factorization of 38198 in exponential form is:

38198 = 2¹ × 71¹ × 269¹

Step-2: 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-3: Factors of 38198

List of positive integer factors of 38198 that divides 38198 without a remainder.

1, 2, 71, 142, 269, 538, 19099

Step-4: Factors of 38208

List of positive integer factors of 38208 that divides 38198 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38198 and 38208. The biggest common factor number is the GCF number.
So the greatest common factor 38198 and 38208 is 2.

Also check out the Least Common Multiple of 38198 and 38208