What is the Greatest Common Factor of 39168 and 39186?

Greatest common factor (GCF) of 39168 and 39186 is 18.

GCF(39168,39186) = 18

We will now calculate the prime factors of 39168 and 39186, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39168 and 39186.

How to find the GCF of 39168 and 39186?

We will first find the prime factorization of 39168 and 39186. After we will calculate the factors of 39168 and 39186 and find the biggest common factor number .

Step-1: Prime Factorization of 39168

Prime factors of 39168 are 2, 3, 17. Prime factorization of 39168 in exponential form is:

39168 = 2⁸ × 3² × 17¹

Step-2: Prime Factorization of 39186

Prime factors of 39186 are 2, 3, 7, 311. Prime factorization of 39186 in exponential form is:

39186 = 2¹ × 3² × 7¹ × 311¹

Step-3: Factors of 39168

List of positive integer factors of 39168 that divides 39168 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 64, 68, 72, 96, 102, 128, 136, 144, 153, 192, 204, 256, 272, 288, 306, 384, 408, 544, 576, 612, 768, 816, 1088, 1152, 1224, 1632, 2176, 2304, 2448, 3264, 4352, 4896, 6528, 9792, 13056, 19584

Step-4: Factors of 39186

List of positive integer factors of 39186 that divides 39168 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 311, 622, 933, 1866, 2177, 2799, 4354, 5598, 6531, 13062, 19593

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39168 and 39186. The biggest common factor number is the GCF number.
So the greatest common factor 39168 and 39186 is 18.

Also check out the Least Common Multiple of 39168 and 39186