What is the Greatest Common Factor of 27314 and 27328?

Greatest common factor (GCF) of 27314 and 27328 is 14.

GCF(27314,27328) = 14

We will now calculate the prime factors of 27314 and 27328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27314 and 27328.

How to find the GCF of 27314 and 27328?

We will first find the prime factorization of 27314 and 27328. After we will calculate the factors of 27314 and 27328 and find the biggest common factor number .

Step-1: Prime Factorization of 27314

Prime factors of 27314 are 2, 7, 1951. Prime factorization of 27314 in exponential form is:

27314 = 2¹ × 7¹ × 1951¹

Step-2: Prime Factorization of 27328

Prime factors of 27328 are 2, 7, 61. Prime factorization of 27328 in exponential form is:

27328 = 2⁶ × 7¹ × 61¹

Step-3: Factors of 27314

List of positive integer factors of 27314 that divides 27314 without a remainder.

1, 2, 7, 14, 1951, 3902, 13657

Step-4: Factors of 27328

List of positive integer factors of 27328 that divides 27314 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 61, 64, 112, 122, 224, 244, 427, 448, 488, 854, 976, 1708, 1952, 3416, 3904, 6832, 13664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27314 and 27328. The biggest common factor number is the GCF number.
So the greatest common factor 27314 and 27328 is 14.

Also check out the Least Common Multiple of 27314 and 27328