What is the Greatest Common Factor of 27750 and 27768?

Greatest common factor (GCF) of 27750 and 27768 is 6.

GCF(27750,27768) = 6

We will now calculate the prime factors of 27750 and 27768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27750 and 27768.

How to find the GCF of 27750 and 27768?

We will first find the prime factorization of 27750 and 27768. After we will calculate the factors of 27750 and 27768 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 27768

Prime factors of 27768 are 2, 3, 13, 89. Prime factorization of 27768 in exponential form is:

27768 = 2³ × 3¹ × 13¹ × 89¹

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 27768

List of positive integer factors of 27768 that divides 27750 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 89, 104, 156, 178, 267, 312, 356, 534, 712, 1068, 1157, 2136, 2314, 3471, 4628, 6942, 9256, 13884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27750 and 27768. The biggest common factor number is the GCF number.
So the greatest common factor 27750 and 27768 is 6.

Also check out the Least Common Multiple of 27750 and 27768