Question

4.25 Lab9d: Factorials

This program will output the factorial of numbers 1 through 10. Recall that 10! = 10 * 9 * 8 * 7 * … * 2 * 1.

Calculating the factorial will require two loops. The outer loop will iterate from the number 1 up to and including the number n. n will be based on a number the user entered (an int value). The inner loop will calculate the factorial of the number the first loop is currently on--go ahead and work it out on paper first! When the inner loop finishes it will have calculated the n's factorial, so now save the value in an array called factorials. [Note that number 1 will be stored in factorials[0], so this requires a little navigation through the mire of being "off by one".

Finally, use a separate for loop to print all the results from the factorials array in the following format: "The factorial of [current number] is [factorial value]"
Make sure to print out a new line between each print out.

Example input:

10

Example output:

The factorial of 1 is 1
The factorial of 2 is 2
The factorial of 3 is 6
The factorial of 4 is 24
The factorial of 5 is 120
The factorial of 6 is 720
The factorial of 7 is 5040
The factorial of 8 is 40320
The factorial of 9 is 362880
The factorial of 10 is 3628800

The factorials array will contain:

factorials[0] is 1
factorials[1] is 2
factorials[2] is 6
factorials[3] is 24
factorials[4] is 120
factorials[5] is 720
factorials[6] is 5040
factorials[7] is 40320
factorials[8] is 362880
factorials[9] is 3628800

import java.util.Scanner;
public class Factorials
{
public static void main (String args[])
{
Scanner scnr = new Scanner(System.in);
int num = scnr.nextInt();
  
// TODO: Create a new array called "factorials" sized "num" elements

// TODO: Loop to calculate the factorial (from 1 to num)
// Store the result in factorials array
// (watch out for index off by one!)


// TODO: Loop to print the "factorials" array with message form:
// "The factorial of X is Y"
}

Answer 1

I have designed and developed the program for the given question using Java. I have included the comments for each part of the code and finally added the output screenshot of the program.

Please look at the comments for better understanding of the program.

OUTPUT:

CODE:

*Factorials.java*

import java.util.Scanner;
public class Factorials
{
public static void main (String args[])
{
Scanner scnr = new Scanner(System.in);
int num = scnr.nextInt();

// TODO: Create a new array called "factorials" sized "num" elements
int factorials[] = new int[num];
  
// TODO: Loop to calculate the factorial (from 1 to num)
// Store the result in factorials array
// (watch out for index off by one!)
   for(int i=1; i<=num; i++){ // outer loop numbered from 1 to num
       factorials[i-1]=1; // initialise the product as 1
for(int j =2; j <=i;j++){ // innerloop calculates the factorial.
// this multiplies the product by 2,3,4,......until 'i'
// Suppose i =5.
// Innerloop calculates factorial[4]=120
// Initially factorial[4]=1.
// Innerloop interates from 2 to 'i'.
// we use factorial[i-1] because we store result of i in factorial[i-1]
// It multiplies the factorial[4] by 2 and store the results in factorial[4].
//Later it multiplies the factorial[4] by 3 and repeats until it is multiplied by 5.
  

factorials[i-1] = factorials[i-1]*j;
}
// therefore now after innerloop finishes,
// factorial[i-1]=1*2*3 . . . . . * i
// Hence for eg., 5! = factorials[4] = 1*2*3*4*5 =120 .
  
}
  

// TODO: Loop to print the "factorials" array with message form:
// "The factorial of X is Y"
// System.out.println() function prints the string specified in it in a newline.
for(int i = 1; i<= num; i++){
// We concatenate several strings using '+' operator.
// The first string is concatenated with 'i' value using '+' and then factorials[i-1] is concatenated.
// since factorial of i is stored in factorials[i-1].
System.out.println("The factorial of "+i+" is "+factorials[i-1]);
}
  
//Please note that this program can only calculate factorials for only upto 15.
// This is due to the integer limits in java int has 4 bytes which holds values from -2,147,483,648 to 2,147,483, 647
// you might have to use other data types or other methods.
// However this solution is correct and complete for your question.
}
}

//-------------------------------------------------------------------------------------

**Thank You. Please comment for any further clarification**