What is the Greatest Common Factor of 30174 and 30192?

Greatest common factor (GCF) of 30174 and 30192 is 6.

GCF(30174,30192) = 6

We will now calculate the prime factors of 30174 and 30192, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30174 and 30192.

How to find the GCF of 30174 and 30192?

We will first find the prime factorization of 30174 and 30192. After we will calculate the factors of 30174 and 30192 and find the biggest common factor number .

Step-1: Prime Factorization of 30174

Prime factors of 30174 are 2, 3, 47, 107. Prime factorization of 30174 in exponential form is:

30174 = 2¹ × 3¹ × 47¹ × 107¹

Step-2: Prime Factorization of 30192

Prime factors of 30192 are 2, 3, 17, 37. Prime factorization of 30192 in exponential form is:

30192 = 2⁴ × 3¹ × 17¹ × 37¹

Step-3: Factors of 30174

List of positive integer factors of 30174 that divides 30174 without a remainder.

1, 2, 3, 6, 47, 94, 107, 141, 214, 282, 321, 642, 5029, 10058, 15087

Step-4: Factors of 30192

List of positive integer factors of 30192 that divides 30174 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 37, 48, 51, 68, 74, 102, 111, 136, 148, 204, 222, 272, 296, 408, 444, 592, 629, 816, 888, 1258, 1776, 1887, 2516, 3774, 5032, 7548, 10064, 15096

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30174 and 30192. The biggest common factor number is the GCF number.
So the greatest common factor 30174 and 30192 is 6.

Also check out the Least Common Multiple of 30174 and 30192