What is the Greatest Common Factor of 300 and 550?

Greatest common factor (GCF) of 300 and 550 is 50.

GCF(300,550) = 50

We will now calculate the prime factors of 300 and 550, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 300 and 550.

How to find the GCF of 300 and 550?

We will first find the prime factorization of 300 and 550. After we will calculate the factors of 300 and 550 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 550

Prime factors of 550 are 2, 5, 11. Prime factorization of 550 in exponential form is:

550 = 2¹ × 5² × 11¹

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 550

List of positive integer factors of 550 that divides 300 without a remainder.

1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 300 and 550. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 550 is 50.

Also check out the Least Common Multiple of 300 and 550