What is the Greatest Common Factor of 4305 and 4314?

Greatest common factor (GCF) of 4305 and 4314 is 3.

GCF(4305,4314) = 3

We will now calculate the prime factors of 4305 and 4314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4305 and 4314.

How to find the GCF of 4305 and 4314?

We will first find the prime factorization of 4305 and 4314. After we will calculate the factors of 4305 and 4314 and find the biggest common factor number .

Step-1: Prime Factorization of 4305

Prime factors of 4305 are 3, 5, 7, 41. Prime factorization of 4305 in exponential form is:

4305 = 3¹ × 5¹ × 7¹ × 41¹

Step-2: Prime Factorization of 4314

Prime factors of 4314 are 2, 3, 719. Prime factorization of 4314 in exponential form is:

4314 = 2¹ × 3¹ × 719¹

Step-3: Factors of 4305

List of positive integer factors of 4305 that divides 4305 without a remainder.

1, 3, 5, 7, 15, 21, 35, 41, 105, 123, 205, 287, 615, 861, 1435

Step-4: Factors of 4314

List of positive integer factors of 4314 that divides 4305 without a remainder.

1, 2, 3, 6, 719, 1438, 2157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4305 and 4314. The biggest common factor number is the GCF number.
So the greatest common factor 4305 and 4314 is 3.

Also check out the Least Common Multiple of 4305 and 4314