What is the Greatest Common Factor of 27756 and 27760?

Greatest common factor (GCF) of 27756 and 27760 is 4.

GCF(27756,27760) = 4

We will now calculate the prime factors of 27756 and 27760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27756 and 27760.

How to find the GCF of 27756 and 27760?

We will first find the prime factorization of 27756 and 27760. After we will calculate the factors of 27756 and 27760 and find the biggest common factor number .

Step-1: Prime Factorization of 27756

Prime factors of 27756 are 2, 3, 257. Prime factorization of 27756 in exponential form is:

27756 = 2² × 3³ × 257¹

Step-2: 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-3: Factors of 27756

List of positive integer factors of 27756 that divides 27756 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 257, 514, 771, 1028, 1542, 2313, 3084, 4626, 6939, 9252, 13878

Step-4: Factors of 27760

List of positive integer factors of 27760 that divides 27756 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27756 and 27760. The biggest common factor number is the GCF number.
So the greatest common factor 27756 and 27760 is 4.

Also check out the Least Common Multiple of 27756 and 27760