What is the Greatest Common Factor of 27760 and 27780?

Greatest common factor (GCF) of 27760 and 27780 is 20.

GCF(27760,27780) = 20

We will now calculate the prime factors of 27760 and 27780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27760 and 27780.

How to find the GCF of 27760 and 27780?

We will first find the prime factorization of 27760 and 27780. After we will calculate the factors of 27760 and 27780 and find the biggest common factor number .

Step-1: Prime Factorization of 27760

Prime factors of 27760 are 2, 5, 347. Prime factorization of 27760 in exponential form is:

27760 = 2⁴ × 5¹ × 347¹

Step-2: Prime Factorization of 27780

Prime factors of 27780 are 2, 3, 5, 463. Prime factorization of 27780 in exponential form is:

27780 = 2² × 3¹ × 5¹ × 463¹

Step-3: Factors of 27760

List of positive integer factors of 27760 that divides 27760 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 347, 694, 1388, 1735, 2776, 3470, 5552, 6940, 13880

Step-4: Factors of 27780

List of positive integer factors of 27780 that divides 27760 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 463, 926, 1389, 1852, 2315, 2778, 4630, 5556, 6945, 9260, 13890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27760 and 27780. The biggest common factor number is the GCF number.
So the greatest common factor 27760 and 27780 is 20.

Also check out the Least Common Multiple of 27760 and 27780