What is the Greatest Common Factor of 27744 and 27758?

Greatest common factor (GCF) of 27744 and 27758 is 2.

GCF(27744,27758) = 2

We will now calculate the prime factors of 27744 and 27758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27744 and 27758.

How to find the GCF of 27744 and 27758?

We will first find the prime factorization of 27744 and 27758. After we will calculate the factors of 27744 and 27758 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 27758

Prime factors of 27758 are 2, 13879. Prime factorization of 27758 in exponential form is:

27758 = 2¹ × 13879¹

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 27758

List of positive integer factors of 27758 that divides 27744 without a remainder.

1, 2, 13879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27744 and 27758. The biggest common factor number is the GCF number.
So the greatest common factor 27744 and 27758 is 2.

Also check out the Least Common Multiple of 27744 and 27758