What is the Greatest Common Factor of 174 and 186?

Greatest common factor (GCF) of 174 and 186 is 6.

GCF(174,186) = 6

We will now calculate the prime factors of 174 and 186, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 174 and 186.

How to find the GCF of 174 and 186?

We will first find the prime factorization of 174 and 186. After we will calculate the factors of 174 and 186 and find the biggest common factor number .

Step-1: Prime Factorization of 174

Prime factors of 174 are 2, 3, 29. Prime factorization of 174 in exponential form is:

174 = 2¹ × 3¹ × 29¹

Step-2: Prime Factorization of 186

Prime factors of 186 are 2, 3, 31. Prime factorization of 186 in exponential form is:

186 = 2¹ × 3¹ × 31¹

Step-3: Factors of 174

List of positive integer factors of 174 that divides 174 without a remainder.

1, 2, 3, 6, 29, 58, 87

Step-4: Factors of 186

List of positive integer factors of 186 that divides 174 without a remainder.

1, 2, 3, 6, 31, 62, 93

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 174 and 186. The biggest common factor number is the GCF number.
So the greatest common factor 174 and 186 is 6.

Also check out the Least Common Multiple of 174 and 186