What is the Greatest Common Factor of 174 and 182?

Greatest common factor (GCF) of 174 and 182 is 2.

GCF(174,182) = 2

We will now calculate the prime factors of 174 and 182, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 174 and 182.

How to find the GCF of 174 and 182?

We will first find the prime factorization of 174 and 182. After we will calculate the factors of 174 and 182 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 182

Prime factors of 182 are 2, 7, 13. Prime factorization of 182 in exponential form is:

182 = 2¹ × 7¹ × 13¹

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 182

List of positive integer factors of 182 that divides 174 without a remainder.

1, 2, 7, 13, 14, 26, 91

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 174 and 182. The biggest common factor number is the GCF number.
So the greatest common factor 174 and 182 is 2.

Also check out the Least Common Multiple of 174 and 182