What is the Greatest Common Factor of 38160 and 38178?

Greatest common factor (GCF) of 38160 and 38178 is 18.

GCF(38160,38178) = 18

We will now calculate the prime factors of 38160 and 38178, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38160 and 38178.

How to find the GCF of 38160 and 38178?

We will first find the prime factorization of 38160 and 38178. After we will calculate the factors of 38160 and 38178 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 38178

Prime factors of 38178 are 2, 3, 7, 101. Prime factorization of 38178 in exponential form is:

38178 = 2¹ × 3³ × 7¹ × 101¹

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 38178

List of positive integer factors of 38178 that divides 38160 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 101, 126, 189, 202, 303, 378, 606, 707, 909, 1414, 1818, 2121, 2727, 4242, 5454, 6363, 12726, 19089

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38160 and 38178. The biggest common factor number is the GCF number.
So the greatest common factor 38160 and 38178 is 18.

Also check out the Least Common Multiple of 38160 and 38178