What is the Greatest Common Factor of 38144 and 38160?

Greatest common factor (GCF) of 38144 and 38160 is 16.

GCF(38144,38160) = 16

We will now calculate the prime factors of 38144 and 38160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38144 and 38160.

How to find the GCF of 38144 and 38160?

We will first find the prime factorization of 38144 and 38160. After we will calculate the factors of 38144 and 38160 and find the biggest common factor number .

Step-1: Prime Factorization of 38144

Prime factors of 38144 are 2, 149. Prime factorization of 38144 in exponential form is:

38144 = 2⁸ × 149¹

Step-2: 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-3: Factors of 38144

List of positive integer factors of 38144 that divides 38144 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 149, 256, 298, 596, 1192, 2384, 4768, 9536, 19072

Step-4: Factors of 38160

List of positive integer factors of 38160 that divides 38144 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38144 and 38160. The biggest common factor number is the GCF number.
So the greatest common factor 38144 and 38160 is 16.

Also check out the Least Common Multiple of 38144 and 38160