Code is returning wrong value for factorials

Question

My code for factorials works fine up until n=13 where it then starts giving me the wrong answer. Does anyone know why?

public class Factorial {
    public static void main(String[] args) {
        System.out.println(factorial(13));
    }

    public static int factorial(int n) {
        for (int i = n - 1; i >= 1; i--) {
            n=n*i;
        }

        return n;
    }    
}

Answer 1

int is finite

Your problem is the 32bit integer limit.

Java's int datatype represents a signed 32bit integer meaning it can store values from -2^31 to 2^31-1 (2 147 483 647)

13! is 6 227 020 800 which is higher than that so it doesn't fit in an int.

long is bigger than int but still finite

In order to fix this, you can use long which represents a signed 64bit integer:

public static long factorial(long n) {
       
    for(int i=(int)n-1;i>=1;i--){
        n=n*i;
 }
    return n;
}

long allows ranges from -2^63 up to 2^63-1 (a number with 18 digits) which allows factorials until 20!.

Get real big with BigInteger

If you want to. go even further, you can use BigInteger:

public static BigInteger factorial(long n) {
    BigInteger value=BigInteger.valueOf(n);
    for(int i=n-1;i>=1;i--){
        value=value.multiply(BigInteger.valueOf(i));
    }
    return value;
}

While BigInteger also isn't infinite (ranging from -2^(2^32) until to -2^(2^32) at minimum), it should be sufficient for your purpose. This is explained in the Javadoc of BigInteger:

BigInteger must support values in the range -2^{Integer.MAX_VALUE} (exclusive) to +2^{Integer.MAX_VALUE} (exclusive)