What is the Greatest Common Factor of 39 and 54?

Greatest common factor (GCF) of 39 and 54 is 3.

GCF(39,54) = 3

We will now calculate the prime factors of 39 and 54, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39 and 54.

How to find the GCF of 39 and 54?

We will first find the prime factorization of 39 and 54. After we will calculate the factors of 39 and 54 and find the biggest common factor number .

Step-1: Prime Factorization of 39

Prime factors of 39 are 3, 13. Prime factorization of 39 in exponential form is:

39 = 3¹ × 13¹

Step-2: Prime Factorization of 54

Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:

54 = 2¹ × 3³

Step-3: Factors of 39

List of positive integer factors of 39 that divides 39 without a remainder.

1, 3, 13

Step-4: Factors of 54

List of positive integer factors of 54 that divides 39 without a remainder.

1, 2, 3, 6, 9, 18, 27

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39 and 54. The biggest common factor number is the GCF number.
So the greatest common factor 39 and 54 is 3.

Also check out the Least Common Multiple of 39 and 54