What is the Greatest Common Factor of 7314 and 7323?

Greatest common factor (GCF) of 7314 and 7323 is 3.

GCF(7314,7323) = 3

We will now calculate the prime factors of 7314 and 7323, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7314 and 7323.

How to find the GCF of 7314 and 7323?

We will first find the prime factorization of 7314 and 7323. After we will calculate the factors of 7314 and 7323 and find the biggest common factor number .

Step-1: Prime Factorization of 7314

Prime factors of 7314 are 2, 3, 23, 53. Prime factorization of 7314 in exponential form is:

7314 = 2¹ × 3¹ × 23¹ × 53¹

Step-2: Prime Factorization of 7323

Prime factors of 7323 are 3, 2441. Prime factorization of 7323 in exponential form is:

7323 = 3¹ × 2441¹

Step-3: Factors of 7314

List of positive integer factors of 7314 that divides 7314 without a remainder.

1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657

Step-4: Factors of 7323

List of positive integer factors of 7323 that divides 7314 without a remainder.

1, 3, 2441

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7314 and 7323. The biggest common factor number is the GCF number.
So the greatest common factor 7314 and 7323 is 3.

Also check out the Least Common Multiple of 7314 and 7323