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Given a number n, count all multiples of 3 and/or 5 in set {1, 2, 3, … n}

  • Last Updated : 03 Nov, 2021

Given a number n, count all multiples of 3 and/or 5 in set of numbers from 1 to n.
Examples: 
 

Input: n = 6
Output: 3
There are three multiples of 3 and/or 5 in {1, 2, 3, 4, 5, 6}

Input: n = 16
Output: 7
There are two multiples of 7 and/or 5 in {1, 2, .. 16}
The multiples are 3, 5, 6, 9, 10, 12, 15

We strongly recommend to minimize your browser and try this yourself first.
The value of n/3 gives us number of multiples of 3, the value of n/5 gives us number of multiples of 5. But the important point is there are may be some common multiples which are multiples of both 3 and 5. We can get such multiples by using n/15. Following is the program to find count of multiples. 
 

C++




// C++ program to find count of multiples of 3 and 5 in {1, 2, 3, ..n}
#include <iostream>
using namespace std;
 
unsigned countOfMultiples(unsigned n)
{
   // Add multiples of 3 and 5.  Since common multiples are
   // counted twice in n/3 + n/15, subtract common multiples
   return (n/3 + n/5 - n/15);
}
 
// Driver program to test above function
int main()
{
   cout << countOfMultiples(6) << endl;
   cout << countOfMultiples(16) << endl;
   return 0;
}

Java




// Java program to find count of multiples
// of 3 and 5 in {1, 2, 3, ..n}
import java .io.*;
class GFG {
     
    static long countOfMultiples(long n)
    {
         
        // Add multiples of 3 and 5.
        // Since common multiples are
        // counted twice in n/3 + n/15,
        // subtract common multiples
        return (n/3 + n/5 - n/15);
    }
     
    // Driver Code
    static public void main (String[] args)
    {
        System.out.println(countOfMultiples(6));
        System.out.println(countOfMultiples(16));
    }
}
 
// This code is contributed by anuj_67.

Python3




# python program to find count
# of multiples of 3 and 5 in
# {1, 2, 3, ..n}
 
def countOfMultiples(n):
    # Add multiples of 3 and 5.
    # Since common multiples are
    # counted twice in n/3 + n/15,
    # subtract common multiples
    return (int(n/3) + int(n/5) - int(n/15));
 
 
# Driver program to test
# above function
print(countOfMultiples(6))
print(countOfMultiples(16))
 
# This code is contributed by Sam007.

C#




// C# program to find count of multiples
// of 3 and 5 in {1, 2, 3, ..n}
using System;
 
public class GFG {
     
    static uint countOfMultiples(uint n)
    {
        // Add multiples of 3 and 5.
        // Since common multiples are
        // counted twice in n/3 + n/15,
        // subtract common multiples
        return (n/3 + n/5 - n/15);
    }
     
    // Driver program to test above
    // function
    static public void Main ()
    {
        Console.WriteLine(countOfMultiples(6));
         
        Console.WriteLine(countOfMultiples(16)) ;
    }
}
 
// This code is contributed by anuj_67.

PHP




<?php
// PHP program to find count of
// multiples of 3 and 5 in
// {1, 2, 3, ..n}
 
function countOfMultiples($n)
{
     
    // Add multiples of 3 and 5.
    // Since common multiples are
    // counted twice in n/3 + n/15,
    // subtract common multiples
    return floor(floor($n / 3) +
                 floor($n / 5) -
                 floor($n / 15));
}
 
// Driver Code
echo countOfMultiples(6),"\n" ;
echo countOfMultiples(16);
 
// This code is contributed by nitin mittal
?>

Javascript




<script>
    // Javascript program to find count of multiples
    // of 3 and 5 in {1, 2, 3, ..n}
     
    function countOfMultiples(n)
    {
        // Add multiples of 3 and 5.
        // Since common multiples are
        // counted twice in n/3 + n/15,
        // subtract common multiples
        return (parseInt(n/3, 10) + parseInt(n/5, 10) - parseInt(n/15, 10));
    }
     
    document.write(countOfMultiples(6) + "</br>");
           
      document.write(countOfMultiples(16) + "</br>") ;
     
</script>

Output: 

3
7

Time Complexity: O(1)

Auxiliary Space: O(1)

This article is contributed by Asif. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
 


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