What is the Greatest Common Factor of 7314 and 7322?

Greatest common factor (GCF) of 7314 and 7322 is 2.

GCF(7314,7322) = 2

We will now calculate the prime factors of 7314 and 7322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7314 and 7322.

How to find the GCF of 7314 and 7322?

We will first find the prime factorization of 7314 and 7322. After we will calculate the factors of 7314 and 7322 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 7322

Prime factors of 7322 are 2, 7, 523. Prime factorization of 7322 in exponential form is:

7322 = 2¹ × 7¹ × 523¹

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 7322

List of positive integer factors of 7322 that divides 7314 without a remainder.

1, 2, 7, 14, 523, 1046, 3661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7314 and 7322. The biggest common factor number is the GCF number.
So the greatest common factor 7314 and 7322 is 2.

Also check out the Least Common Multiple of 7314 and 7322