What is the Greatest Common Factor of 54 and 69?

Greatest common factor (GCF) of 54 and 69 is 3.

GCF(54,69) = 3

We will now calculate the prime factors of 54 and 69, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54 and 69.

How to find the GCF of 54 and 69?

We will first find the prime factorization of 54 and 69. After we will calculate the factors of 54 and 69 and find the biggest common factor number .

Step-1: Prime Factorization of 54

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

54 = 2¹ × 3³

Step-2: Prime Factorization of 69

Prime factors of 69 are 3, 23. Prime factorization of 69 in exponential form is:

69 = 3¹ × 23¹

Step-3: Factors of 54

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

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

Step-4: Factors of 69

List of positive integer factors of 69 that divides 54 without a remainder.

1, 3, 23

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54 and 69. The biggest common factor number is the GCF number.
So the greatest common factor 54 and 69 is 3.

Also check out the Least Common Multiple of 54 and 69