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 numbersbool 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 aboveint 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 numbersimport java.util.*;class GFG{// Number of single digit prime numbersstatic int SIZE = 4;// function to check whether a number can// be expressed as a product of single // digit numbersstatic 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 abovepublic 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 numbersSIZE = 4# function to check whether# a number can be# expressed as a product# of single digit numbersdef 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 == 1n = 24if 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 numbersusing 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 numbersfunction 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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