What is the Greatest Common Factor of 300 and 310?

Greatest common factor (GCF) of 300 and 310 is 10.

GCF(300,310) = 10

We will now calculate the prime factors of 300 and 310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 300 and 310.

How to find the GCF of 300 and 310?

We will first find the prime factorization of 300 and 310. After we will calculate the factors of 300 and 310 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 310

Prime factors of 310 are 2, 5, 31. Prime factorization of 310 in exponential form is:

310 = 2¹ × 5¹ × 31¹

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 310

List of positive integer factors of 310 that divides 300 without a remainder.

1, 2, 5, 10, 31, 62, 155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 300 and 310. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 310 is 10.

Also check out the Least Common Multiple of 300 and 310