What is the Greatest Common Factor of 27744 and 27761?

Greatest common factor (GCF) of 27744 and 27761 is 17.

GCF(27744,27761) = 17

We will now calculate the prime factors of 27744 and 27761, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27744 and 27761.

How to find the GCF of 27744 and 27761?

We will first find the prime factorization of 27744 and 27761. After we will calculate the factors of 27744 and 27761 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27761

Prime factors of 27761 are 17, 23, 71. Prime factorization of 27761 in exponential form is:

27761 = 17¹ × 23¹ × 71¹

Step-3: Factors of 27744

List of positive integer factors of 27744 that divides 27744 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

Step-4: Factors of 27761

List of positive integer factors of 27761 that divides 27744 without a remainder.

1, 17, 23, 71, 391, 1207, 1633

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27744 and 27761. The biggest common factor number is the GCF number.
So the greatest common factor 27744 and 27761 is 17.

Also check out the Least Common Multiple of 27744 and 27761