What is the Greatest Common Factor of 27075 and 27084?

Greatest common factor (GCF) of 27075 and 27084 is 3.

GCF(27075,27084) = 3

We will now calculate the prime factors of 27075 and 27084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27075 and 27084.

How to find the GCF of 27075 and 27084?

We will first find the prime factorization of 27075 and 27084. After we will calculate the factors of 27075 and 27084 and find the biggest common factor number .

Step-1: Prime Factorization of 27075

Prime factors of 27075 are 3, 5, 19. Prime factorization of 27075 in exponential form is:

27075 = 3¹ × 5² × 19²

Step-2: Prime Factorization of 27084

Prime factors of 27084 are 2, 3, 37, 61. Prime factorization of 27084 in exponential form is:

27084 = 2² × 3¹ × 37¹ × 61¹

Step-3: Factors of 27075

List of positive integer factors of 27075 that divides 27075 without a remainder.

1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 361, 475, 1083, 1425, 1805, 5415, 9025

Step-4: Factors of 27084

List of positive integer factors of 27084 that divides 27075 without a remainder.

1, 2, 3, 4, 6, 12, 37, 61, 74, 111, 122, 148, 183, 222, 244, 366, 444, 732, 2257, 4514, 6771, 9028, 13542

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27075 and 27084. The biggest common factor number is the GCF number.
So the greatest common factor 27075 and 27084 is 3.

Also check out the Least Common Multiple of 27075 and 27084