What is the Greatest Common Factor of 27 and 33?

Greatest common factor (GCF) of 27 and 33 is 3.

GCF(27,33) = 3

We will now calculate the prime factors of 27 and 33, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27 and 33.

How to find the GCF of 27 and 33?

We will first find the prime factorization of 27 and 33. After we will calculate the factors of 27 and 33 and find the biggest common factor number .

Step-1: Prime Factorization of 27

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 3³

Step-2: Prime Factorization of 33

Prime factors of 33 are 3, 11. Prime factorization of 33 in exponential form is:

33 = 3¹ × 11¹

Step-3: Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1, 3, 9

Step-4: Factors of 33

List of positive integer factors of 33 that divides 27 without a remainder.

1, 3, 11

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27 and 33. The biggest common factor number is the GCF number.
So the greatest common factor 27 and 33 is 3.

Also check out the Least Common Multiple of 27 and 33