What is the Greatest Common Factor of 30 and 180?

Greatest common factor (GCF) of 30 and 180 is 30.

GCF(30,180) = 30

We will now calculate the prime factors of 30 and 180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30 and 180.

How to find the GCF of 30 and 180?

We will first find the prime factorization of 30 and 180. After we will calculate the factors of 30 and 180 and find the biggest common factor number .

Step-1: Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

30 = 2¹ × 3¹ × 5¹

Step-2: 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-3: Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15

Step-4: Factors of 180

List of positive integer factors of 180 that divides 30 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 180. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 180 is 30.

Also check out the Least Common Multiple of 30 and 180