What is the Greatest Common Factor of 300 and 315?

Greatest common factor (GCF) of 300 and 315 is 15.

GCF(300,315) = 15

We will now calculate the prime factors of 300 and 315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 300 and 315.

How to find the GCF of 300 and 315?

We will first find the prime factorization of 300 and 315. After we will calculate the factors of 300 and 315 and find the biggest common factor number .

Step-1: Prime Factorization of 300

Prime factors of 300 are 2, 3, 5. Prime factorization of 300 in exponential form is:

300 = 2² × 3¹ × 5²

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 300

List of positive integer factors of 300 that divides 300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150

Step-4: Factors of 315

List of positive integer factors of 315 that divides 300 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 300 and 315. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 315 is 15.

Also check out the Least Common Multiple of 300 and 315