What is the Greatest Common Factor of 165 and 174?

Greatest common factor (GCF) of 165 and 174 is 3.

GCF(165,174) = 3

We will now calculate the prime factors of 165 and 174, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 165 and 174.

How to find the GCF of 165 and 174?

We will first find the prime factorization of 165 and 174. After we will calculate the factors of 165 and 174 and find the biggest common factor number .

Step-1: Prime Factorization of 165

Prime factors of 165 are 3, 5, 11. Prime factorization of 165 in exponential form is:

165 = 3¹ × 5¹ × 11¹

Step-2: 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-3: Factors of 165

List of positive integer factors of 165 that divides 165 without a remainder.

1, 3, 5, 11, 15, 33, 55

Step-4: Factors of 174

List of positive integer factors of 174 that divides 165 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 165 and 174. The biggest common factor number is the GCF number.
So the greatest common factor 165 and 174 is 3.

Also check out the Least Common Multiple of 165 and 174