Normal integer data types can't store the result of large factorials, we need to use an array to represent the digits individually to perform a digit-by-digit multiplication. When multiplying with the next number in the factorial calculation, multiply each digit of the current result with the new number, handling carries appropriately. Algorithm outline:
Initialize:
Create an array to store the digits of the result.
Set the initial value of the array to 1.
Loop through numbers to multiply:
For each number from 2 to the desired number (n), iterate through the digits of the current result array.
Multiply each digit with the current number, adding any carry from the previous multiplication.
Update the result array with the new digits and carry.