public static string Problem3()
{
Console.WriteLine("\n\t3) What is the largest prime factor of the number 600,851,475,143?");
int diviser = 2;
// This number will be divided several times until it cannot be divided by numbers other than 1 and itself,
// which means we have found the biggest prime factor of the initial value.
long numberToBeDivided = 600851475143;
int initialValueSqrt = (int)Math.Sqrt(numberToBeDivided);// A prime factor of a number cannot be larger that the number's square root.
for (int i = 0; i < initialValueSqrt; i++)
{
// The numberToBeDivided is divided by the same diviser for as long as the number is divisible by that specific diviser.
while (numberToBeDivided % diviser == 0)
{
numberToBeDivided /= diviser;
}
if (MathyHelper.IsPrime(numberToBeDivided))
{
break;
}
// If the numberToBeDivided is not divisable by the current diviser anymore but it is not a prime number, we move onto the next diviser.
diviser++;
}
return(numberToBeDivided.ToString());
}
public static string Problem5()
{
Console.WriteLine("\n\t5) What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?");
for (int i = 20; i < int.MaxValue; i += 20)
{
if (MathyHelper.IsDivisibleFrom1To20(i))
{
return(i.ToString());
}
}
return("Unable to find the answer.");
}
public static string Problem7()
{
Console.WriteLine("\n\t7) What is the 10,001st prime number?");
long number = 3;
int counter = 1; // 2 is already counted.
while (counter != 10001)
{
if (MathyHelper.IsPrime(number))
{
counter++;
}
number += 2;
}
return((number - 2).ToString());
}
public static string Problem4()
{
Console.WriteLine("\n\t4) Find the largest palindrome made from the product of two 3 digit numbers.");
int currentProduct;
int greatestProduct = 0;
// These loops iterate through every single possible combination of 3-digit numbers and multiplays them.
for (int i = 999; i > 99; i--)
{
// Second loop always starts with whatever the value of i is since we have already calculated all the multiplication combinations of the previous i.
for (int j = i; j > 99; j--)
{
currentProduct = i * j;
if (MathyHelper.IsPalendromic(currentProduct.ToString()) && currentProduct > greatestProduct)
{
greatestProduct = currentProduct;
}
}
}
return(greatestProduct.ToString());
}