What is the Greatest Common Factor of 54069 and 54075?

Greatest common factor (GCF) of 54069 and 54075 is 3.

GCF(54069,54075) = 3

We will now calculate the prime factors of 54069 and 54075, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54069 and 54075.

How to find the GCF of 54069 and 54075?

We will first find the prime factorization of 54069 and 54075. After we will calculate the factors of 54069 and 54075 and find the biggest common factor number .

Step-1: Prime Factorization of 54069

Prime factors of 54069 are 3, 67, 269. Prime factorization of 54069 in exponential form is:

54069 = 3¹ × 67¹ × 269¹

Step-2: Prime Factorization of 54075

Prime factors of 54075 are 3, 5, 7, 103. Prime factorization of 54075 in exponential form is:

54075 = 3¹ × 5² × 7¹ × 103¹

Step-3: Factors of 54069

List of positive integer factors of 54069 that divides 54069 without a remainder.

1, 3, 67, 201, 269, 807, 18023

Step-4: Factors of 54075

List of positive integer factors of 54075 that divides 54069 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 75, 103, 105, 175, 309, 515, 525, 721, 1545, 2163, 2575, 3605, 7725, 10815, 18025

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54069 and 54075. The biggest common factor number is the GCF number.
So the greatest common factor 54069 and 54075 is 3.

Also check out the Least Common Multiple of 54069 and 54075