What is the Greatest Common Factor of 180 and 195?

Greatest common factor (GCF) of 180 and 195 is 15.

GCF(180,195) = 15

We will now calculate the prime factors of 180 and 195, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 180 and 195.

How to find the GCF of 180 and 195?

We will first find the prime factorization of 180 and 195. After we will calculate the factors of 180 and 195 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 195

Prime factors of 195 are 3, 5, 13. Prime factorization of 195 in exponential form is:

195 = 3¹ × 5¹ × 13¹

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 195

List of positive integer factors of 195 that divides 180 without a remainder.

1, 3, 5, 13, 15, 39, 65

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 180 and 195. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 195 is 15.

Also check out the Least Common Multiple of 180 and 195