What is the Greatest Common Factor of 1323 and 1338?

Greatest common factor (GCF) of 1323 and 1338 is 3.

GCF(1323,1338) = 3

We will now calculate the prime factors of 1323 and 1338, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1323 and 1338.

How to find the GCF of 1323 and 1338?

We will first find the prime factorization of 1323 and 1338. After we will calculate the factors of 1323 and 1338 and find the biggest common factor number .

Step-1: Prime Factorization of 1323

Prime factors of 1323 are 3, 7. Prime factorization of 1323 in exponential form is:

1323 = 3³ × 7²

Step-2: Prime Factorization of 1338

Prime factors of 1338 are 2, 3, 223. Prime factorization of 1338 in exponential form is:

1338 = 2¹ × 3¹ × 223¹

Step-3: Factors of 1323

List of positive integer factors of 1323 that divides 1323 without a remainder.

1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441

Step-4: Factors of 1338

List of positive integer factors of 1338 that divides 1323 without a remainder.

1, 2, 3, 6, 223, 446, 669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1323 and 1338. The biggest common factor number is the GCF number.
So the greatest common factor 1323 and 1338 is 3.

Also check out the Least Common Multiple of 1323 and 1338