What is the Greatest Common Factor of 38304 and 38324?

Greatest common factor (GCF) of 38304 and 38324 is 4.

GCF(38304,38324) = 4

We will now calculate the prime factors of 38304 and 38324, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38304 and 38324.

How to find the GCF of 38304 and 38324?

We will first find the prime factorization of 38304 and 38324. After we will calculate the factors of 38304 and 38324 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 38324

Prime factors of 38324 are 2, 11, 13, 67. Prime factorization of 38324 in exponential form is:

38324 = 2² × 11¹ × 13¹ × 67¹

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 38324

List of positive integer factors of 38324 that divides 38304 without a remainder.

1, 2, 4, 11, 13, 22, 26, 44, 52, 67, 134, 143, 268, 286, 572, 737, 871, 1474, 1742, 2948, 3484, 9581, 19162

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38304 and 38324. The biggest common factor number is the GCF number.
So the greatest common factor 38304 and 38324 is 4.

Also check out the Least Common Multiple of 38304 and 38324