What is the Greatest Common Factor of 27745 and 27750?

Greatest common factor (GCF) of 27745 and 27750 is 5.

GCF(27745,27750) = 5

We will now calculate the prime factors of 27745 and 27750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27745 and 27750.

How to find the GCF of 27745 and 27750?

We will first find the prime factorization of 27745 and 27750. After we will calculate the factors of 27745 and 27750 and find the biggest common factor number .

Step-1: Prime Factorization of 27745

Prime factors of 27745 are 5, 31, 179. Prime factorization of 27745 in exponential form is:

27745 = 5¹ × 31¹ × 179¹

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 27745

List of positive integer factors of 27745 that divides 27745 without a remainder.

1, 5, 31, 155, 179, 895, 5549

Step-4: Factors of 27750

List of positive integer factors of 27750 that divides 27745 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 27745 and 27750. The biggest common factor number is the GCF number.
So the greatest common factor 27745 and 27750 is 5.

Also check out the Least Common Multiple of 27745 and 27750