Question

This is more of a mathematical and a GMAT/CAT question rather than a programming one. But found this question very interesting and found it from Project Euler.

Before seeing the solution, please try out yourselves.

Let me reiterate the question,

“Find a number which has more than 500 factors. The number is part of a triangle series or natural series of additions”

Triangular number is given a name since it can fill every point in a triangle and will add up like this,

1+2+3+4…+n = n(n+1)/2

The above is sometimes called arithmetic series sum as well.

If you need some mathematical background about finding factors, see the below video,

Answer

I really loved the second brute force method given in the above video since its simple and easier to visualize and program.

I got into lots of problem since I didn’t make up the triangular number in my mind after I got that clear, zoom I got the answer. Number of trails would be at least 20 times. :)

First tried manually using calculators. But it didn’t work out since I didn’t see that I need to calculate only for triangular number.

Do the second method of factorizing start from 1 and go up by triangular series and count the number of factors.

The Method is,

1. find sqrt(number)

2. If the sqrt is a perfect square, then set diff to –1

3. run a loop from 1 to sqrt(number) and count how many numbers are dividing the triangular number selected

4. count*2+diff gives the total factors.

Code

#include <math.h>

void main(int argc, char* argv[])

{

int data=0; //pow(35.00,13.00);

` int next=1;`

` int max = 0;`

` while(1) {`

` int count=0;`

` int diff = 0;`

data = data+next;

int mid = (int) floor(sqrt((double)data));

` if(mid * mid == data) `

diff = -1;

for(int j=1;j<=mid;j++) {

` if(data % j == 0) {`

++count;

}

}

count = count*2+diff;

` if(count > max) {`

max = count;

` cout<<data<<"="<<count<<endl;`

` if(max > 499) `

` break;`

}

next++;

}

}