What is the Greatest Common Factor of 300 and 360?

Greatest common factor (GCF) of 300 and 360 is 60.

GCF(300,360) = 60

We will now calculate the prime factors of 300 and 360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 300 and 360.

How to find the GCF of 300 and 360?

We will first find the prime factorization of 300 and 360. After we will calculate the factors of 300 and 360 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 360

Prime factors of 360 are 2, 3, 5. Prime factorization of 360 in exponential form is:

360 = 2³ × 3² × 5¹

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 360

List of positive integer factors of 360 that divides 300 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 300 and 360. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 360 is 60.

Also check out the Least Common Multiple of 300 and 360