What is the Greatest Common Factor of 300 and 320?

Greatest common factor (GCF) of 300 and 320 is 20.

GCF(300,320) = 20

We will now calculate the prime factors of 300 and 320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 300 and 320.

How to find the GCF of 300 and 320?

We will first find the prime factorization of 300 and 320. After we will calculate the factors of 300 and 320 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 320

Prime factors of 320 are 2, 5. Prime factorization of 320 in exponential form is:

320 = 2⁶ × 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 320

List of positive integer factors of 320 that divides 300 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 300 and 320. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 320 is 20.

Also check out the Least Common Multiple of 300 and 320