What is the Greatest Common Factor of 1299 and 1305?

Greatest common factor (GCF) of 1299 and 1305 is 3.

GCF(1299,1305) = 3

We will now calculate the prime factors of 1299 and 1305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1299 and 1305.

How to find the GCF of 1299 and 1305?

We will first find the prime factorization of 1299 and 1305. After we will calculate the factors of 1299 and 1305 and find the biggest common factor number .

Step-1: Prime Factorization of 1299

Prime factors of 1299 are 3, 433. Prime factorization of 1299 in exponential form is:

1299 = 3¹ × 433¹

Step-2: 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-3: Factors of 1299

List of positive integer factors of 1299 that divides 1299 without a remainder.

1, 3, 433

Step-4: Factors of 1305

List of positive integer factors of 1305 that divides 1299 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1299 and 1305. The biggest common factor number is the GCF number.
So the greatest common factor 1299 and 1305 is 3.

Also check out the Least Common Multiple of 1299 and 1305