What is the Greatest Common Factor of 36 and 216?

Greatest common factor (GCF) of 36 and 216 is 36.

GCF(36,216) = 36

We will now calculate the prime factors of 36 and 216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36 and 216.

How to find the GCF of 36 and 216?

We will first find the prime factorization of 36 and 216. After we will calculate the factors of 36 and 216 and find the biggest common factor number .

Step-1: Prime Factorization of 36

Prime factors of 36 are 2, 3. Prime factorization of 36 in exponential form is:

36 = 2² × 3²

Step-2: Prime Factorization of 216

Prime factors of 216 are 2, 3. Prime factorization of 216 in exponential form is:

216 = 2³ × 3³

Step-3: Factors of 36

List of positive integer factors of 36 that divides 36 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18

Step-4: Factors of 216

List of positive integer factors of 216 that divides 36 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36 and 216. The biggest common factor number is the GCF number.
So the greatest common factor 36 and 216 is 36.

Also check out the Least Common Multiple of 36 and 216