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

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

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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++

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// 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 multples 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;
}

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Java

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// 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 multples 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.

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Python3

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# 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 multples 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.

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C#

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// 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 multples 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.

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PHP

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<?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 multples 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
?>

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Output:

3
7

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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Improved By : Sam007, nitin mittal, vt_m

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