Prime factorization, changing output. - c

Question

Hello guys i have this code.
#include <stdio.h>
#include <stdlib.h>
int main()
{
unsigned int num,i,j;
int a=0;
printf("Please input a number: ");
scanf("%d",&num);
printf("The Prime Factorization: ");
for (i=2;i<=num;i++){
if (num%i==0){
a=1;
if (i==num){
printf(" %ld ",num);
} else {
printf(" %ld *",i);
num/=i;
}
}
}
if (a==0){
printf("%ld ",num);
}
return 0;
}
so let's say i input 40,
it gives me
The Prime Factorization: 2 * 4 * 5
this is correct but, how could I make it output the "2 * 4 * 5"
as "2 ^ 3 * 5"?

Answer 1

Since a prime can appear more than once in the factorization you can't just move on to the next candidate without first testing the current prime until the number is no longer divisble by it.
And to get the nice printout you're after, you can keep a count variable as shown below:
#include <stdio.h>
int main(void) {
unsigned int num,i,count;
int a=0;
printf("Please input a number: ");
scanf("%d",&num);
printf("The Prime Factorization: ");
i = 2;
while(num>1){
if (num%i==0){
a=1;
count = 1;
num /= i;
// Exhaust each prime fully:
while (num%i==0) {
count++;
num /= i;
}
printf("%ld",i);
if (count > 1) {
printf(" ^ %ld", count);
}
if (num > 1) {
printf(" * ");
}
}
i++;
}
if (a==0){
printf("%ld ",num);
}
return 0;
}

Answer 2

something like this:
#include <stdio.h>
#include <stdlib.h>
int main()
{
int num,i,j,count=0;
int a=0;
printf("Please input a number: ");
scanf("%d",&num);
printf("The Prime Factorization: ");
for (i=2;i<=num;i++){
count=0;
a=0;
while(num%i==0){
a=1;
++count;
num/=i;
}
if(a==1)
{
printf("%d ^ %d *",i,count);
}
}
if (a==0){
printf("%ld ",num);
}
return 0;
}