What is the Greatest Common Factor of 314 and 324?

Greatest common factor (GCF) of 314 and 324 is 2.

GCF(314,324) = 2

We will now calculate the prime factors of 314 and 324, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 314 and 324.

How to find the GCF of 314 and 324?

We will first find the prime factorization of 314 and 324. After we will calculate the factors of 314 and 324 and find the biggest common factor number .

Step-1: Prime Factorization of 314

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

314 = 2¹ × 157¹

Step-2: Prime Factorization of 324

Prime factors of 324 are 2, 3. Prime factorization of 324 in exponential form is:

324 = 2² × 3⁴

Step-3: Factors of 314

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

1, 2, 157

Step-4: Factors of 324

List of positive integer factors of 324 that divides 314 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 314 and 324. The biggest common factor number is the GCF number.
So the greatest common factor 314 and 324 is 2.

Also check out the Least Common Multiple of 314 and 324