What is the Greatest Common Factor of 180 and 186?

Greatest common factor (GCF) of 180 and 186 is 6.

GCF(180,186) = 6

We will now calculate the prime factors of 180 and 186, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 180 and 186.

How to find the GCF of 180 and 186?

We will first find the prime factorization of 180 and 186. After we will calculate the factors of 180 and 186 and find the biggest common factor number .

Step-1: Prime Factorization of 180

Prime factors of 180 are 2, 3, 5. Prime factorization of 180 in exponential form is:

180 = 2² × 3² × 5¹

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 180

List of positive integer factors of 180 that divides 180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90

Step-4: Factors of 186

List of positive integer factors of 186 that divides 180 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 180 and 186. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 186 is 6.

Also check out the Least Common Multiple of 180 and 186