What is the Greatest Common Factor of 27740 and 27759?

Greatest common factor (GCF) of 27740 and 27759 is 19.

GCF(27740,27759) = 19

We will now calculate the prime factors of 27740 and 27759, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27740 and 27759.

How to find the GCF of 27740 and 27759?

We will first find the prime factorization of 27740 and 27759. After we will calculate the factors of 27740 and 27759 and find the biggest common factor number .

Step-1: Prime Factorization of 27740

Prime factors of 27740 are 2, 5, 19, 73. Prime factorization of 27740 in exponential form is:

27740 = 2² × 5¹ × 19¹ × 73¹

Step-2: Prime Factorization of 27759

Prime factors of 27759 are 3, 19, 487. Prime factorization of 27759 in exponential form is:

27759 = 3¹ × 19¹ × 487¹

Step-3: Factors of 27740

List of positive integer factors of 27740 that divides 27740 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 73, 76, 95, 146, 190, 292, 365, 380, 730, 1387, 1460, 2774, 5548, 6935, 13870

Step-4: Factors of 27759

List of positive integer factors of 27759 that divides 27740 without a remainder.

1, 3, 19, 57, 487, 1461, 9253

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27740 and 27759. The biggest common factor number is the GCF number.
So the greatest common factor 27740 and 27759 is 19.

Also check out the Least Common Multiple of 27740 and 27759