What is the Greatest Common Factor of 300 and 675?

Greatest common factor (GCF) of 300 and 675 is 75.

GCF(300,675) = 75

We will now calculate the prime factors of 300 and 675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 300 and 675.

How to find the GCF of 300 and 675?

We will first find the prime factorization of 300 and 675. After we will calculate the factors of 300 and 675 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 675

Prime factors of 675 are 3, 5. Prime factorization of 675 in exponential form is:

675 = 3³ × 5²

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 675

List of positive integer factors of 675 that divides 300 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 300 and 675. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 675 is 75.

Also check out the Least Common Multiple of 300 and 675