What is the Greatest Common Factor of 38304 and 38315?

Greatest common factor (GCF) of 38304 and 38315 is 1.

GCF(38304,38315) = 1

We will now calculate the prime factors of 38304 and 38315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38304 and 38315.

How to find the GCF of 38304 and 38315?

We will first find the prime factorization of 38304 and 38315. After we will calculate the factors of 38304 and 38315 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 38315

Prime factors of 38315 are 5, 79, 97. Prime factorization of 38315 in exponential form is:

38315 = 5¹ × 79¹ × 97¹

Step-3: Factors of 38304

List of positive integer factors of 38304 that divides 38304 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

Step-4: Factors of 38315

List of positive integer factors of 38315 that divides 38304 without a remainder.

1, 5, 79, 97, 395, 485, 7663

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38304 and 38315. The biggest common factor number is the GCF number.
So the greatest common factor 38304 and 38315 is 1.

Also check out the Least Common Multiple of 38304 and 38315