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

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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++

// 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;
}

Java

// 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 */

Python3

# 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.

C#

// 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

Javascript

<script>
// javascript implementation to check whether
// a number can be expressed as a 
// product of single digit numbers
 
    // Number of single digit prime numbers
    const SIZE = 4;
 
    // function to check whether a number can
    // be expressed as a product of single
    // digit numbers
    function productOfSingelDgt(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
        var prime = [ 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 program to test above
        var n = 24;
        if (productOfSingelDgt(n))
            document.write("Yes");
        else
            document.write("No");
 
// This code is contributed by gauravrajput1 
</script>

PHP

<?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
?>

Output:

Yes

Time Complexity: O(num), where num is the number of prime factors (2, 3, 5, 7) of n.
Auxiliary space: O(1) as it is using constant space

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