What is the Greatest Common Factor of 38288 and 38304?

Greatest common factor (GCF) of 38288 and 38304 is 16.

GCF(38288,38304) = 16

We will now calculate the prime factors of 38288 and 38304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38288 and 38304.

How to find the GCF of 38288 and 38304?

We will first find the prime factorization of 38288 and 38304. After we will calculate the factors of 38288 and 38304 and find the biggest common factor number .

Step-1: Prime Factorization of 38288

Prime factors of 38288 are 2, 2393. Prime factorization of 38288 in exponential form is:

38288 = 2⁴ × 2393¹

Step-2: Prime Factorization of 38304

Prime factors of 38304 are 2, 3, 7, 19. Prime factorization of 38304 in exponential form is:

38304 = 2⁵ × 3² × 7¹ × 19¹

Step-3: Factors of 38288

List of positive integer factors of 38288 that divides 38288 without a remainder.

1, 2, 4, 8, 16, 2393, 4786, 9572, 19144

Step-4: Factors of 38304

List of positive integer factors of 38304 that divides 38288 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 19, 21, 24, 28, 32, 36, 38, 42, 48, 56, 57, 63, 72, 76, 84, 96, 112, 114, 126, 133, 144, 152, 168, 171, 224, 228, 252, 266, 288, 304, 336, 342, 399, 456, 504, 532, 608, 672, 684, 798, 912, 1008, 1064, 1197, 1368, 1596, 1824, 2016, 2128, 2394, 2736, 3192, 4256, 4788, 5472, 6384, 9576, 12768, 19152

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38288 and 38304. The biggest common factor number is the GCF number.
So the greatest common factor 38288 and 38304 is 16.

Also check out the Least Common Multiple of 38288 and 38304