What is the Greatest Common Factor of 7314 and 7330?

Greatest common factor (GCF) of 7314 and 7330 is 2.

GCF(7314,7330) = 2

We will now calculate the prime factors of 7314 and 7330, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7314 and 7330.

How to find the GCF of 7314 and 7330?

We will first find the prime factorization of 7314 and 7330. After we will calculate the factors of 7314 and 7330 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 7330

Prime factors of 7330 are 2, 5, 733. Prime factorization of 7330 in exponential form is:

7330 = 2¹ × 5¹ × 733¹

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 7330

List of positive integer factors of 7330 that divides 7314 without a remainder.

1, 2, 5, 10, 733, 1466, 3665

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7314 and 7330. The biggest common factor number is the GCF number.
So the greatest common factor 7314 and 7330 is 2.

Also check out the Least Common Multiple of 7314 and 7330