What is the Greatest Common Factor of 1314 and 1328?

Greatest common factor (GCF) of 1314 and 1328 is 2.

GCF(1314,1328) = 2

We will now calculate the prime factors of 1314 and 1328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1314 and 1328.

How to find the GCF of 1314 and 1328?

We will first find the prime factorization of 1314 and 1328. After we will calculate the factors of 1314 and 1328 and find the biggest common factor number .

Step-1: Prime Factorization of 1314

Prime factors of 1314 are 2, 3, 73. Prime factorization of 1314 in exponential form is:

1314 = 2¹ × 3² × 73¹

Step-2: Prime Factorization of 1328

Prime factors of 1328 are 2, 83. Prime factorization of 1328 in exponential form is:

1328 = 2⁴ × 83¹

Step-3: Factors of 1314

List of positive integer factors of 1314 that divides 1314 without a remainder.

1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657

Step-4: Factors of 1328

List of positive integer factors of 1328 that divides 1314 without a remainder.

1, 2, 4, 8, 16, 83, 166, 332, 664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1314 and 1328. The biggest common factor number is the GCF number.
So the greatest common factor 1314 and 1328 is 2.

Also check out the Least Common Multiple of 1314 and 1328