What is the Greatest Common Factor of 305 and 315?

Greatest common factor (GCF) of 305 and 315 is 5.

GCF(305,315) = 5

We will now calculate the prime factors of 305 and 315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 305 and 315.

How to find the GCF of 305 and 315?

We will first find the prime factorization of 305 and 315. After we will calculate the factors of 305 and 315 and find the biggest common factor number .

Step-1: Prime Factorization of 305

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

305 = 5¹ × 61¹

Step-2: Prime Factorization of 315

Prime factors of 315 are 3, 5, 7. Prime factorization of 315 in exponential form is:

315 = 3² × 5¹ × 7¹

Step-3: Factors of 305

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

1, 5, 61

Step-4: Factors of 315

List of positive integer factors of 315 that divides 305 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 305 and 315. The biggest common factor number is the GCF number.
So the greatest common factor 305 and 315 is 5.

Also check out the Least Common Multiple of 305 and 315