What is the Greatest Common Factor of 27735 and 27750?

Greatest common factor (GCF) of 27735 and 27750 is 15.

GCF(27735,27750) = 15

We will now calculate the prime factors of 27735 and 27750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27735 and 27750.

How to find the GCF of 27735 and 27750?

We will first find the prime factorization of 27735 and 27750. After we will calculate the factors of 27735 and 27750 and find the biggest common factor number .

Step-1: Prime Factorization of 27735

Prime factors of 27735 are 3, 5, 43. Prime factorization of 27735 in exponential form is:

27735 = 3¹ × 5¹ × 43²

Step-2: Prime Factorization of 27750

Prime factors of 27750 are 2, 3, 5, 37. Prime factorization of 27750 in exponential form is:

27750 = 2¹ × 3¹ × 5³ × 37¹

Step-3: Factors of 27735

List of positive integer factors of 27735 that divides 27735 without a remainder.

1, 3, 5, 15, 43, 129, 215, 645, 1849, 5547, 9245

Step-4: Factors of 27750

List of positive integer factors of 27750 that divides 27735 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 37, 50, 74, 75, 111, 125, 150, 185, 222, 250, 370, 375, 555, 750, 925, 1110, 1850, 2775, 4625, 5550, 9250, 13875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27735 and 27750. The biggest common factor number is the GCF number.
So the greatest common factor 27735 and 27750 is 15.

Also check out the Least Common Multiple of 27735 and 27750