Technology

Problem 1

Question

Add all the natural numbers below one thousand that are multiples of 3 or 5.

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

 

Solution

 

This problem calls for the sum of all natural numbers that are multiples of 3 or 5 below 1000. The smallest number which is a multiple of 3 or 5 is 3. So my starting number is 3. The terminating condition is also given in the problem as below 1000. Consider the following things while programming

1. Check whether the number is a multiple of 3.

2. Check if the number is multiple of 5 and not a multiple of 3.(This step is to avoid adding duplicate numbers).

 

Finding the sum of all multiples of 3 or 5 below 20.

Initially sum=0

3 is the smallest number that is a multiple of 3 or 5.

 

Number	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
3	Y			Y			Y			Y			Y			Y
5			Y					Y					Y

(Note: Shaded box represents that the number is divisible by either 3 or 5 or both.)

15 is divisible by 3 and 5, so it is sufficient to check and add only once.

 

 

Program

#include<stdio.h>
int main() 
{
    int sum,number;
    sum=0;
    for(number=3;number<1000;number++) {
        if((number%3)==0)   sum=sum+number;
        else if((number%5)==0)  sum=sum+number;
    }
    printf("sum :%d",sum);
    return 0;
}

Output