What is the Greatest Common Factor of 54075 and 54084?

Greatest common factor (GCF) of 54075 and 54084 is 3.

GCF(54075,54084) = 3

We will now calculate the prime factors of 54075 and 54084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54075 and 54084.

How to find the GCF of 54075 and 54084?

We will first find the prime factorization of 54075 and 54084. After we will calculate the factors of 54075 and 54084 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54084

Prime factors of 54084 are 2, 3, 4507. Prime factorization of 54084 in exponential form is:

54084 = 2² × 3¹ × 4507¹

Step-3: Factors of 54075

List of positive integer factors of 54075 that divides 54075 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

Step-4: Factors of 54084

List of positive integer factors of 54084 that divides 54075 without a remainder.

1, 2, 3, 4, 6, 12, 4507, 9014, 13521, 18028, 27042

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54075 and 54084. The biggest common factor number is the GCF number.
So the greatest common factor 54075 and 54084 is 3.

Also check out the Least Common Multiple of 54075 and 54084