What is the Greatest Common Factor of 7300 and 7314?

Greatest common factor (GCF) of 7300 and 7314 is 2.

GCF(7300,7314) = 2

We will now calculate the prime factors of 7300 and 7314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7300 and 7314.

How to find the GCF of 7300 and 7314?

We will first find the prime factorization of 7300 and 7314. After we will calculate the factors of 7300 and 7314 and find the biggest common factor number .

Step-1: Prime Factorization of 7300

Prime factors of 7300 are 2, 5, 73. Prime factorization of 7300 in exponential form is:

7300 = 2² × 5² × 73¹

Step-2: 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-3: Factors of 7300

List of positive integer factors of 7300 that divides 7300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 73, 100, 146, 292, 365, 730, 1460, 1825, 3650

Step-4: Factors of 7314

List of positive integer factors of 7314 that divides 7300 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7300 and 7314. The biggest common factor number is the GCF number.
So the greatest common factor 7300 and 7314 is 2.

Also check out the Least Common Multiple of 7300 and 7314