What is the Greatest Common Factor of 1305 and 1314?

Greatest common factor (GCF) of 1305 and 1314 is 9.

GCF(1305,1314) = 9

We will now calculate the prime factors of 1305 and 1314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1305 and 1314.

How to find the GCF of 1305 and 1314?

We will first find the prime factorization of 1305 and 1314. After we will calculate the factors of 1305 and 1314 and find the biggest common factor number .

Step-1: Prime Factorization of 1305

Prime factors of 1305 are 3, 5, 29. Prime factorization of 1305 in exponential form is:

1305 = 3² × 5¹ × 29¹

Step-2: Prime Factorization of 1314

Prime factors of 1314 are 2, 3, 73. Prime factorization of 1314 in exponential form is:

1314 = 2¹ × 3² × 73¹

Step-3: Factors of 1305

List of positive integer factors of 1305 that divides 1305 without a remainder.

1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435

Step-4: Factors of 1314

List of positive integer factors of 1314 that divides 1305 without a remainder.

1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1305 and 1314. The biggest common factor number is the GCF number.
So the greatest common factor 1305 and 1314 is 9.

Also check out the Least Common Multiple of 1305 and 1314