What is the Greatest Common Factor of 174 and 178?

Greatest common factor (GCF) of 174 and 178 is 2.

GCF(174,178) = 2

We will now calculate the prime factors of 174 and 178, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 174 and 178.

How to find the GCF of 174 and 178?

We will first find the prime factorization of 174 and 178. After we will calculate the factors of 174 and 178 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 178

Prime factors of 178 are 2, 89. Prime factorization of 178 in exponential form is:

178 = 2¹ × 89¹

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 178

List of positive integer factors of 178 that divides 174 without a remainder.

1, 2, 89

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 174 and 178. The biggest common factor number is the GCF number.
So the greatest common factor 174 and 178 is 2.

Also check out the Least Common Multiple of 174 and 178