What is the Greatest Common Factor of 180 and 200?

Greatest common factor (GCF) of 180 and 200 is 20.

GCF(180,200) = 20

We will now calculate the prime factors of 180 and 200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 180 and 200.

How to find the GCF of 180 and 200?

We will first find the prime factorization of 180 and 200. After we will calculate the factors of 180 and 200 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 200

Prime factors of 200 are 2, 5. Prime factorization of 200 in exponential form is:

200 = 2³ × 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 200

List of positive integer factors of 200 that divides 180 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 180 and 200. The biggest common factor number is the GCF number.
So the greatest common factor 180 and 200 is 20.

Also check out the Least Common Multiple of 180 and 200