What is the Greatest Common Factor of 39168 and 39174?

Greatest common factor (GCF) of 39168 and 39174 is 6.

GCF(39168,39174) = 6

We will now calculate the prime factors of 39168 and 39174, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39168 and 39174.

How to find the GCF of 39168 and 39174?

We will first find the prime factorization of 39168 and 39174. After we will calculate the factors of 39168 and 39174 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 39174

Prime factors of 39174 are 2, 3, 6529. Prime factorization of 39174 in exponential form is:

39174 = 2¹ × 3¹ × 6529¹

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 39174

List of positive integer factors of 39174 that divides 39168 without a remainder.

1, 2, 3, 6, 6529, 13058, 19587

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39168 and 39174. The biggest common factor number is the GCF number.
So the greatest common factor 39168 and 39174 is 6.

Also check out the Least Common Multiple of 39168 and 39174