What is the Greatest Common Factor of 300 and 314?

Greatest common factor (GCF) of 300 and 314 is 2.

GCF(300,314) = 2

We will now calculate the prime factors of 300 and 314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 300 and 314.

How to find the GCF of 300 and 314?

We will first find the prime factorization of 300 and 314. After we will calculate the factors of 300 and 314 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 314

Prime factors of 314 are 2, 157. Prime factorization of 314 in exponential form is:

314 = 2¹ × 157¹

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 314

List of positive integer factors of 314 that divides 300 without a remainder.

1, 2, 157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 300 and 314. The biggest common factor number is the GCF number.
So the greatest common factor 300 and 314 is 2.

Also check out the Least Common Multiple of 300 and 314