What is the Greatest Common Factor of 27750 and 27764?

Greatest common factor (GCF) of 27750 and 27764 is 2.

GCF(27750,27764) = 2

We will now calculate the prime factors of 27750 and 27764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27750 and 27764.

How to find the GCF of 27750 and 27764?

We will first find the prime factorization of 27750 and 27764. After we will calculate the factors of 27750 and 27764 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27764

Prime factors of 27764 are 2, 11, 631. Prime factorization of 27764 in exponential form is:

27764 = 2² × 11¹ × 631¹

Step-3: Factors of 27750

List of positive integer factors of 27750 that divides 27750 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

Step-4: Factors of 27764

List of positive integer factors of 27764 that divides 27750 without a remainder.

1, 2, 4, 11, 22, 44, 631, 1262, 2524, 6941, 13882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27750 and 27764. The biggest common factor number is the GCF number.
So the greatest common factor 27750 and 27764 is 2.

Also check out the Least Common Multiple of 27750 and 27764