What is the Greatest Common Factor of 38292 and 38304?

Greatest common factor (GCF) of 38292 and 38304 is 12.

GCF(38292,38304) = 12

We will now calculate the prime factors of 38292 and 38304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38292 and 38304.

How to find the GCF of 38292 and 38304?

We will first find the prime factorization of 38292 and 38304. After we will calculate the factors of 38292 and 38304 and find the biggest common factor number .

Step-1: Prime Factorization of 38292

Prime factors of 38292 are 2, 3, 3191. Prime factorization of 38292 in exponential form is:

38292 = 2² × 3¹ × 3191¹

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 38292

List of positive integer factors of 38292 that divides 38292 without a remainder.

1, 2, 3, 4, 6, 12, 3191, 6382, 9573, 12764, 19146

Step-4: Factors of 38304

List of positive integer factors of 38304 that divides 38292 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 38292 and 38304. The biggest common factor number is the GCF number.
So the greatest common factor 38292 and 38304 is 12.

Also check out the Least Common Multiple of 38292 and 38304