What is the Greatest Common Factor of 48 and 180?

Greatest common factor (GCF) of 48 and 180 is 12.

GCF(48,180) = 12

We will now calculate the prime factors of 48 and 180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48 and 180.

How to find the GCF of 48 and 180?

We will first find the prime factorization of 48 and 180. After we will calculate the factors of 48 and 180 and find the biggest common factor number .

Step-1: Prime Factorization of 48

Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:

48 = 2⁴ × 3¹

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 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24

Step-4: Factors of 180

List of positive integer factors of 180 that divides 48 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 48 and 180. The biggest common factor number is the GCF number.
So the greatest common factor 48 and 180 is 12.

Also check out the Least Common Multiple of 48 and 180