What is the Greatest Common Factor of 38192 and 38208?

Greatest common factor (GCF) of 38192 and 38208 is 16.

GCF(38192,38208) = 16

We will now calculate the prime factors of 38192 and 38208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38192 and 38208.

How to find the GCF of 38192 and 38208?

We will first find the prime factorization of 38192 and 38208. After we will calculate the factors of 38192 and 38208 and find the biggest common factor number .

Step-1: Prime Factorization of 38192

Prime factors of 38192 are 2, 7, 11, 31. Prime factorization of 38192 in exponential form is:

38192 = 2⁴ × 7¹ × 11¹ × 31¹

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 38192

List of positive integer factors of 38192 that divides 38192 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 31, 44, 56, 62, 77, 88, 112, 124, 154, 176, 217, 248, 308, 341, 434, 496, 616, 682, 868, 1232, 1364, 1736, 2387, 2728, 3472, 4774, 5456, 9548, 19096

Step-4: Factors of 38208

List of positive integer factors of 38208 that divides 38192 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 38192 and 38208. The biggest common factor number is the GCF number.
So the greatest common factor 38192 and 38208 is 16.

Also check out the Least Common Multiple of 38192 and 38208