Check whether a number can be expressed as a product of single digit numbers

Given a non-negative number n. The problem is to check whether the given number n can be expressed as a product of single digit numbers or not.

Examples:

Input : n = 24
Output : Yes
Different combinations are:
(8*3) and (6*4)

Input : 68
Output : No
To represent 68 as product of 
number, 17 must be included which
is a two digit number.



Approach: We have to check whether the number n has no prime factors other than 2, 3, 5, 7. For this we repeatedly divide the number n by (2, 3, 5, 7) until it cannot be further divided by these numbers. After this process if n == 1, then it can be expressed as a product of single digit numbers, else if it is greater than 1, then it cannot be expressed.

C++

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// C++ implementation to check whether a number can be
// expressed as a product of single digit numbers
#include <bits/stdc++.h>
using namespace std;
  
// Number of single digit prime numbers
#define SIZE 4
  
// function to check whether a number can be
// expressed as a product of single digit numbers
bool productOfSingelDgt(int n)
{
    // if 'n' is a single digit number, then
    // it can be expressed
    if (n >= 0 && n <= 9)
        return true;
  
    // define single digit prime numbers array
    int prime[] = { 2, 3, 5, 7 };
  
    // repeatedly divide 'n' by the given prime 
    // numbers until all the numbers are used 
    // or 'n' > 1
    for (int i = 0; i < SIZE && n > 1; i++)
        while (n % prime[i] == 0)
            n = n / prime[i];
  
    // if true, then 'n' can
    // be expressed
    return (n == 1);
}
  
// Driver program to test above
int main()
{
    int n = 24;
    productOfSingelDgt(n)? cout << "Yes"
                           cout << "No";
    return 0;
}

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Java

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// Java implementation to check whether
// a number can be expressed as a 
// product of single digit numbers
import java.util.*;
  
class GFG
{
  
// Number of single digit prime numbers
static int SIZE = 4;
  
// function to check whether a number can
// be expressed as a product of single 
// digit numbers
static boolean productOfSingelDgt(int n)
{
    // if 'n' is a single digit number, 
    // then it can be expressed
    if (n >= 0 && n <= 9)
        return true;
  
    // define single digit prime numbers
    // array
    int[] prime = { 2, 3, 5, 7 };
  
    // repeatedly divide 'n' by the given
    // prime numbers until all the numbers
    // are used or 'n' > 1
    for (int i = 0; i < SIZE && n > 1; i++)
        while (n % prime[i] == 0)
            n = n / prime[i];
  
    // if true, then 'n' can
    // be expressed
    return (n == 1);
}
  
// Driver program to test above
public static void main (String[] args) 
{
    int n = 24;
    if(productOfSingelDgt(n))
    System.out.println("Yes");
    else
    System.out.println("No"); 
}
      
}
/* This code is contributed by Mr. Somesh Awasthi */

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Python3

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# Python3 program to check
# whether a number can be
# expressed as a product of
# single digit numbers
  
# Number of single digit
# prime numbers
SIZE = 4
  
# function to check whether
# a number can be
# expressed as a product
# of single digit numbers
def productOfSingelDgt(n):
  
    # if 'n' is a single digit
        # number, then
    # it can be expressed
    if n >= 0 and n <= 9:
        return True
  
    # define single digit prime
        # numbers array
    prime = [ 2, 3, 5, 7 ]
  
    # repeatedly divide 'n' by
        # the given prime 
    # numbers until all the 
        # numbers are used 
    # or 'n' > 1
    i = 0
    while i < SIZE and n > 1:
        while n % prime[i] == 0:
            n = n / prime[i]
        i += 1
  
    # if true, then 'n' can
    # be expressed
    return n == 1
  
n = 24
if productOfSingelDgt(n):
    print ("Yes")
else :
    print ("No")
  
# This code is contributed
# by Shreyanshi Arun.

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C#

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// C# implementation to check whether
// a number can be expressed as a
// product of single digit numbers
using System;
  
class GFG {
  
    // Number of single digit prime numbers
    static int SIZE = 4;
  
    // function to check whether a number can
    // be expressed as a product of single
    // digit numbers
    static bool productOfSingelDgt(int n)
    {
        // if 'n' is a single digit number,
        // then it can be expressed
        if (n >= 0 && n <= 9)
            return true;
  
        // define single digit prime numbers
        // array
        int[] prime = { 2, 3, 5, 7 };
  
        // repeatedly divide 'n' by the given
        // prime numbers until all the numbers
        // are used or 'n' > 1
        for (int i = 0; i < SIZE && n > 1; i++)
            while (n % prime[i] == 0)
                n = n / prime[i];
  
        // if true, then 'n' can
        // be expressed
        return (n == 1);
    }
  
    // Driver program to test above
    public static void Main()
    {
        int n = 24;
        if (productOfSingelDgt(n))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
  
}
  
// This code is contributed by Sam007

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PHP

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<?php
// PHP implementation to check
// whether a number can be 
// expressed as a product of 
// single digit numbers
  
// function to check whether
// a number can be expressed 
//as a product of single 
// digit numbers
function productOfSingelDgt($n,$SIZE)
{
      
    // if 'n' is a single
    // digit number, then
    // it can be expressed
    if ($n >= 0 && $n <= 9)
        return true;
  
    // define single digit 
    // prime numbers array
    $prime = array(2, 3, 5, 7);
  
    // repeatedly divide 'n' 
    // by the given prime 
    // numbers until all 
    // the numbers are used 
    // or 'n' > 1
    for ($i = 0; $i < $SIZE && $n > 1; $i++)
        while ($n % $prime[$i] == 0)
            $n = $n / $prime[$i];
  
    // if true, then 'n' can
    // be expressed
    return ($n == 1);
}
  
    // Driver Code
    $SIZE = 4;
    $n = 24;
    if(productOfSingelDgt($n, $SIZE))
        echo "Yes" ;
    else
        echo "No";
  
// This code is contributed by Sam007
?>

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Output:

Yes

Time Complexity: O(num), where num is the number of prime factors (2, 3, 5, 7) of n.

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Improved By : Sam007