What is the Greatest Common Factor of 10304 and 10312?

Greatest common factor (GCF) of 10304 and 10312 is 8.

GCF(10304,10312) = 8

We will now calculate the prime factors of 10304 and 10312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10304 and 10312.

How to find the GCF of 10304 and 10312?

We will first find the prime factorization of 10304 and 10312. After we will calculate the factors of 10304 and 10312 and find the biggest common factor number .

Step-1: Prime Factorization of 10304

Prime factors of 10304 are 2, 7, 23. Prime factorization of 10304 in exponential form is:

10304 = 2⁶ × 7¹ × 23¹

Step-2: Prime Factorization of 10312

Prime factors of 10312 are 2, 1289. Prime factorization of 10312 in exponential form is:

10312 = 2³ × 1289¹

Step-3: Factors of 10304

List of positive integer factors of 10304 that divides 10304 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 64, 92, 112, 161, 184, 224, 322, 368, 448, 644, 736, 1288, 1472, 2576, 5152

Step-4: Factors of 10312

List of positive integer factors of 10312 that divides 10304 without a remainder.

1, 2, 4, 8, 1289, 2578, 5156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10304 and 10312. The biggest common factor number is the GCF number.
So the greatest common factor 10304 and 10312 is 8.

Also check out the Least Common Multiple of 10304 and 10312