What is the Greatest Common Factor of 38160 and 38176?

Greatest common factor (GCF) of 38160 and 38176 is 16.

GCF(38160,38176) = 16

We will now calculate the prime factors of 38160 and 38176, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38160 and 38176.

How to find the GCF of 38160 and 38176?

We will first find the prime factorization of 38160 and 38176. After we will calculate the factors of 38160 and 38176 and find the biggest common factor number .

Step-1: Prime Factorization of 38160

Prime factors of 38160 are 2, 3, 5, 53. Prime factorization of 38160 in exponential form is:

38160 = 2⁴ × 3² × 5¹ × 53¹

Step-2: Prime Factorization of 38176

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

38176 = 2⁵ × 1193¹

Step-3: Factors of 38160

List of positive integer factors of 38160 that divides 38160 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 53, 60, 72, 80, 90, 106, 120, 144, 159, 180, 212, 240, 265, 318, 360, 424, 477, 530, 636, 720, 795, 848, 954, 1060, 1272, 1590, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 6360, 7632, 9540, 12720, 19080

Step-4: Factors of 38176

List of positive integer factors of 38176 that divides 38160 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38160 and 38176. The biggest common factor number is the GCF number.
So the greatest common factor 38160 and 38176 is 16.

Also check out the Least Common Multiple of 38160 and 38176