What is the Greatest Common Factor of 27728 and 27744?

Greatest common factor (GCF) of 27728 and 27744 is 16.

GCF(27728,27744) = 16

We will now calculate the prime factors of 27728 and 27744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27728 and 27744.

How to find the GCF of 27728 and 27744?

We will first find the prime factorization of 27728 and 27744. After we will calculate the factors of 27728 and 27744 and find the biggest common factor number .

Step-1: Prime Factorization of 27728

Prime factors of 27728 are 2, 1733. Prime factorization of 27728 in exponential form is:

27728 = 2⁴ × 1733¹

Step-2: Prime Factorization of 27744

Prime factors of 27744 are 2, 3, 17. Prime factorization of 27744 in exponential form is:

27744 = 2⁵ × 3¹ × 17²

Step-3: Factors of 27728

List of positive integer factors of 27728 that divides 27728 without a remainder.

1, 2, 4, 8, 16, 1733, 3466, 6932, 13864

Step-4: Factors of 27744

List of positive integer factors of 27744 that divides 27728 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 68, 96, 102, 136, 204, 272, 289, 408, 544, 578, 816, 867, 1156, 1632, 1734, 2312, 3468, 4624, 6936, 9248, 13872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27728 and 27744. The biggest common factor number is the GCF number.
So the greatest common factor 27728 and 27744 is 16.

Also check out the Least Common Multiple of 27728 and 27744