What is the Greatest Common Factor of 1338 and 1353?

Greatest common factor (GCF) of 1338 and 1353 is 3.

GCF(1338,1353) = 3

We will now calculate the prime factors of 1338 and 1353, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1338 and 1353.

How to find the GCF of 1338 and 1353?

We will first find the prime factorization of 1338 and 1353. After we will calculate the factors of 1338 and 1353 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1353

Prime factors of 1353 are 3, 11, 41. Prime factorization of 1353 in exponential form is:

1353 = 3¹ × 11¹ × 41¹

Step-3: Factors of 1338

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

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

Step-4: Factors of 1353

List of positive integer factors of 1353 that divides 1338 without a remainder.

1, 3, 11, 33, 41, 123, 451

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1338 and 1353. The biggest common factor number is the GCF number.
So the greatest common factor 1338 and 1353 is 3.

Also check out the Least Common Multiple of 1338 and 1353