What is the Greatest Common Factor of 180 and 225?

Greatest common factor (GCF) of 180 and 225 is 45.

GCF(180,225) = 45

We will now calculate the prime factors of 180 and 225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 180 and 225.

How to find the GCF of 180 and 225?

We will first find the prime factorization of 180 and 225. After we will calculate the factors of 180 and 225 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 225

Prime factors of 225 are 3, 5. Prime factorization of 225 in exponential form is:

225 = 3² × 5²

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 225

List of positive integer factors of 225 that divides 180 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 180 and 225. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 225 is 45.

Also check out the Least Common Multiple of 180 and 225