What is the Greatest Common Factor of 312 and 321?

Greatest common factor (GCF) of 312 and 321 is 3.

GCF(312,321) = 3

We will now calculate the prime factors of 312 and 321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 312 and 321.

How to find the GCF of 312 and 321?

We will first find the prime factorization of 312 and 321. After we will calculate the factors of 312 and 321 and find the biggest common factor number .

Step-1: Prime Factorization of 312

Prime factors of 312 are 2, 3, 13. Prime factorization of 312 in exponential form is:

312 = 2³ × 3¹ × 13¹

Step-2: Prime Factorization of 321

Prime factors of 321 are 3, 107. Prime factorization of 321 in exponential form is:

321 = 3¹ × 107¹

Step-3: Factors of 312

List of positive integer factors of 312 that divides 312 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156

Step-4: Factors of 321

List of positive integer factors of 321 that divides 312 without a remainder.

1, 3, 107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 312 and 321. The biggest common factor number is the GCF number.
So the greatest common factor 312 and 321 is 3.

Also check out the Least Common Multiple of 312 and 321