What is the Greatest Common Factor of 7314 and 7334?

Greatest common factor (GCF) of 7314 and 7334 is 2.

GCF(7314,7334) = 2

We will now calculate the prime factors of 7314 and 7334, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7314 and 7334.

How to find the GCF of 7314 and 7334?

We will first find the prime factorization of 7314 and 7334. After we will calculate the factors of 7314 and 7334 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 7334

Prime factors of 7334 are 2, 19, 193. Prime factorization of 7334 in exponential form is:

7334 = 2¹ × 19¹ × 193¹

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 7334

List of positive integer factors of 7334 that divides 7314 without a remainder.

1, 2, 19, 38, 193, 386, 3667

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7314 and 7334. The biggest common factor number is the GCF number.
So the greatest common factor 7314 and 7334 is 2.

Also check out the Least Common Multiple of 7314 and 7334