What is the Greatest Common Factor of 27750 and 27762?

Greatest common factor (GCF) of 27750 and 27762 is 6.

GCF(27750,27762) = 6

We will now calculate the prime factors of 27750 and 27762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27750 and 27762.

How to find the GCF of 27750 and 27762?

We will first find the prime factorization of 27750 and 27762. After we will calculate the factors of 27750 and 27762 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 27762

Prime factors of 27762 are 2, 3, 7, 661. Prime factorization of 27762 in exponential form is:

27762 = 2¹ × 3¹ × 7¹ × 661¹

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 27762

List of positive integer factors of 27762 that divides 27750 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 661, 1322, 1983, 3966, 4627, 9254, 13881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27750 and 27762. The biggest common factor number is the GCF number.
So the greatest common factor 27750 and 27762 is 6.

Also check out the Least Common Multiple of 27750 and 27762