What is the Greatest Common Factor of 299 and 305?

Greatest common factor (GCF) of 299 and 305 is 1.

GCF(299,305) = 1

We will now calculate the prime factors of 299 and 305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 299 and 305.

How to find the GCF of 299 and 305?

We will first find the prime factorization of 299 and 305. After we will calculate the factors of 299 and 305 and find the biggest common factor number .

Step-1: Prime Factorization of 299

Prime factors of 299 are 13, 23. Prime factorization of 299 in exponential form is:

299 = 13¹ × 23¹

Step-2: Prime Factorization of 305

Prime factors of 305 are 5, 61. Prime factorization of 305 in exponential form is:

305 = 5¹ × 61¹

Step-3: Factors of 299

List of positive integer factors of 299 that divides 299 without a remainder.

1, 13, 23

Step-4: Factors of 305

List of positive integer factors of 305 that divides 299 without a remainder.

1, 5, 61

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 299 and 305. The biggest common factor number is the GCF number.
So the greatest common factor 299 and 305 is 1.

Also check out the Least Common Multiple of 299 and 305