What is the Greatest Common Factor of 27525 and 27540?

Greatest common factor (GCF) of 27525 and 27540 is 15.

GCF(27525,27540) = 15

We will now calculate the prime factors of 27525 and 27540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27525 and 27540.

How to find the GCF of 27525 and 27540?

We will first find the prime factorization of 27525 and 27540. After we will calculate the factors of 27525 and 27540 and find the biggest common factor number .

Step-1: Prime Factorization of 27525

Prime factors of 27525 are 3, 5, 367. Prime factorization of 27525 in exponential form is:

27525 = 3¹ × 5² × 367¹

Step-2: Prime Factorization of 27540

Prime factors of 27540 are 2, 3, 5, 17. Prime factorization of 27540 in exponential form is:

27540 = 2² × 3⁴ × 5¹ × 17¹

Step-3: Factors of 27525

List of positive integer factors of 27525 that divides 27525 without a remainder.

1, 3, 5, 15, 25, 75, 367, 1101, 1835, 5505, 9175

Step-4: Factors of 27540

List of positive integer factors of 27540 that divides 27525 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 27, 30, 34, 36, 45, 51, 54, 60, 68, 81, 85, 90, 102, 108, 135, 153, 162, 170, 180, 204, 255, 270, 306, 324, 340, 405, 459, 510, 540, 612, 765, 810, 918, 1020, 1377, 1530, 1620, 1836, 2295, 2754, 3060, 4590, 5508, 6885, 9180, 13770

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27525 and 27540. The biggest common factor number is the GCF number.
So the greatest common factor 27525 and 27540 is 15.

Also check out the Least Common Multiple of 27525 and 27540