What is the Greatest Common Factor of 180 and 185?

Greatest common factor (GCF) of 180 and 185 is 5.

GCF(180,185) = 5

We will now calculate the prime factors of 180 and 185, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 180 and 185.

How to find the GCF of 180 and 185?

We will first find the prime factorization of 180 and 185. After we will calculate the factors of 180 and 185 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 185

Prime factors of 185 are 5, 37. Prime factorization of 185 in exponential form is:

185 = 5¹ × 37¹

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 185

List of positive integer factors of 185 that divides 180 without a remainder.

1, 5, 37

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 180 and 185. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 185 is 5.

Also check out the Least Common Multiple of 180 and 185