void factor(int I) {
 
    int P = 1;
    int mult;
 
    while (I > 1) {
 
          P = P+1;
          I = I/P;
 
          while (I%P != 0) {
                 P = P+1;
                 I = I/P;
          }
 
          cout << P << " with multiplicity ";
 
          mult = 1;
 
          while (I%P == 0) {
                 I = I/P;
                 mult++;
          }
 
          cout << mult << endl;
    }
 
}

void factorise(bigInt I) {
 
     bigInt one(1); // used to increment big ints
     bigInt zero;   // find if a bigInt equals zero
     bigInt result;
     bigInt temp(I);
     bigInt P(1);
     bigInt R(1);
     bigInt mult;
 
     while (!I.lessOrEqual(one)) {  
 
           P = P.add(one); 
           temp = I;
 
           temp.divide(P,temp,R);
 
           if (!R.isEqual(zero)) { // MAY NEED TO CHANGE TO IF STATEMENT
               temp.divide(P,temp,R); 
               P = P.add(one);
           }
 
           // Now P is the smallest prime factors of I
           P.writeBigInt();  // OR I.writeBigInt();
           cout << " with multiplicity ";
 
           mult = one;
 
           I.divide(P,temp,R);
 
           //while (R.isEqual(zero)) {
             while (!I.lessOrEqual(P)) { // && !R.isEqual(zero)) {
                  I.divide(P,I,R);
                  mult = mult.add(one);    
           }
 
           mult.writeBigInt();
           cout << endl;
 
     }
 
}
 
void fact(bigInt I) {
 
     bigInt one(1); // used to increment big ints
     bigInt zero;   // find if a bigInt equals zero
     bigInt result;
     bigInt temp(I);
     bigInt P(1);
     bigInt R(1);
     bigInt mult(1);
 
     while (!I.lessOrEqual(one)) {
           temp = I;
         while (one.lessThan(temp)) {
 
 
                temp.divide(P,temp,R);
                P = P.add(one);
                if (R.isEqual(zero) && one.lessThan(temp)) {
                    break;
                }     
          }
 
          P.writeBigInt();  // OR I.writeBigInt();
           cout << " with multiplicity ";
 
          mult = one;
 
          while (!I.lessOrEqual(P) && !R.isEqual(zero)) {
                I.divide(P,I,R);
                mult = mult.add(one);
          }
 
          mult.writeBigInt();
           cout << endl;
     }
}
 
void factor(int I) {
 
    int P = 1;
    int mult;
 
    while (I > 1) {
 
          P = P+1;
          I = I/P;
 
          while (I%P != 0) {
                 P = P+1;
                 I = I/P;
          }
 
          cout << P << " with multiplicity ";
 
          mult = 1;
 
          while (I%P == 0) {
                 I = I/P;
                 mult++;
          }
 
          cout << mult << endl;
    }
 
}

#include <iostream>
 
int main()
{
  //an example input
  int I = 40;
 
  //find the smallest P that divides I evenly
  int P = 2;
 
  while(I % P != 0)
  {
    P++;
  }
 
  //output the smallest P that was found
  std::cout << P << std::endl;
 
  //show what P multiplied by everything up until the correct amount
  int mult = 1;
  while(mult * P <= I)
  {
    std::cout << mult << " * " << P << " = " << mult*P <<std::endl;
    mult++;
  }
 
  return 0;
}

An outline of the above algorithm would look something like:
 
// positive integer I is given
P = 1 //determines when a even factor of I is found
while (I > 1) //I is you input number
{
P = P + 1// p is now 2
if I mod P != 0 go back to previous statement //if I mod p == 1 then increment P until a factor is found
 
// now P is the smallest prime factor of I //now you found a factor for I
display P //show the factor 
mult = 1 
exactly divide I by P as often as is possible, //keep diving I by the even factor until you get a decimal division
assigning to I the result of each exact division, //now you need to find another factor of that number, so start repeating from the start
 
and incrementing mult with each exact division
display mult, end line
}