What is the Greatest Common Factor of 7314 and 7324?

Greatest common factor (GCF) of 7314 and 7324 is 2.

GCF(7314,7324) = 2

We will now calculate the prime factors of 7314 and 7324, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7314 and 7324.

How to find the GCF of 7314 and 7324?

We will first find the prime factorization of 7314 and 7324. After we will calculate the factors of 7314 and 7324 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 7324

Prime factors of 7324 are 2, 1831. Prime factorization of 7324 in exponential form is:

7324 = 2² × 1831¹

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 7324

List of positive integer factors of 7324 that divides 7314 without a remainder.

1, 2, 4, 1831, 3662

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7314 and 7324. The biggest common factor number is the GCF number.
So the greatest common factor 7314 and 7324 is 2.

Also check out the Least Common Multiple of 7314 and 7324