What is the Greatest Common Factor of 30168 and 30174?

Greatest common factor (GCF) of 30168 and 30174 is 6.

GCF(30168,30174) = 6

We will now calculate the prime factors of 30168 and 30174, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30168 and 30174.

How to find the GCF of 30168 and 30174?

We will first find the prime factorization of 30168 and 30174. After we will calculate the factors of 30168 and 30174 and find the biggest common factor number .

Step-1: Prime Factorization of 30168

Prime factors of 30168 are 2, 3, 419. Prime factorization of 30168 in exponential form is:

30168 = 2³ × 3² × 419¹

Step-2: 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-3: Factors of 30168

List of positive integer factors of 30168 that divides 30168 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 419, 838, 1257, 1676, 2514, 3352, 3771, 5028, 7542, 10056, 15084

Step-4: Factors of 30174

List of positive integer factors of 30174 that divides 30168 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30168 and 30174. The biggest common factor number is the GCF number.
So the greatest common factor 30168 and 30174 is 6.

Also check out the Least Common Multiple of 30168 and 30174