What is the Greatest Common Factor of 177 and 186?

Greatest common factor (GCF) of 177 and 186 is 3.

GCF(177,186) = 3

We will now calculate the prime factors of 177 and 186, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 177 and 186.

How to find the GCF of 177 and 186?

We will first find the prime factorization of 177 and 186. After we will calculate the factors of 177 and 186 and find the biggest common factor number .

Step-1: Prime Factorization of 177

Prime factors of 177 are 3, 59. Prime factorization of 177 in exponential form is:

177 = 3¹ × 59¹

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 177

List of positive integer factors of 177 that divides 177 without a remainder.

1, 3, 59

Step-4: Factors of 186

List of positive integer factors of 186 that divides 177 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 177 and 186. The biggest common factor number is the GCF number.
So the greatest common factor 177 and 186 is 3.

Also check out the Least Common Multiple of 177 and 186