What is the Greatest Common Factor of 38176 and 38192?

Greatest common factor (GCF) of 38176 and 38192 is 16.

GCF(38176,38192) = 16

We will now calculate the prime factors of 38176 and 38192, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38176 and 38192.

How to find the GCF of 38176 and 38192?

We will first find the prime factorization of 38176 and 38192. After we will calculate the factors of 38176 and 38192 and find the biggest common factor number .

Step-1: Prime Factorization of 38176

Prime factors of 38176 are 2, 1193. Prime factorization of 38176 in exponential form is:

38176 = 2⁵ × 1193¹

Step-2: 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-3: Factors of 38176

List of positive integer factors of 38176 that divides 38176 without a remainder.

1, 2, 4, 8, 16, 32, 1193, 2386, 4772, 9544, 19088

Step-4: Factors of 38192

List of positive integer factors of 38192 that divides 38176 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38176 and 38192. The biggest common factor number is the GCF number.
So the greatest common factor 38176 and 38192 is 16.

Also check out the Least Common Multiple of 38176 and 38192