# Count of prime digits of a Number which divides the number

Given an integer **N**, the task is to count the number of digits in N which is a prime number, and also divides the number.**Examples:**

Input:N = 12Output:1Explanation:

Digits of the number = {1, 2}

But, only 2 is prime number that divides N.Input:N = 1032Output:2Explanation:

Digits of the number = {1, 0, 3, 2}

3 and 2 divides the number and are also prime.

**Naive Approach:** The idea is to find all the digits of the number. For each digit, check if is prime or not. If yes, then check if it divides the number or not. If both the cases are true, then increment the count by 1. The final count is the required answer.**Efficient Approach:** Since only 2, 3, 5, and 7 are the prime single-digit numbers, therefore for each digit, check if divides the number and if is 2, 3, 5 or 7. If both the cases are true, then increment the count by 1. The final count is the required answer.

Below is the implementation of this approach:

## C++

`// C++ program to count number of digits` `// which is prime and also divides number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the number of` `// digits in number which divides the` `// number and is also a prime number` `int` `countDigit(` `int` `n)` `{` ` ` `bool` `prime[10];` ` ` `memset` `(prime, ` `false` `, ` `sizeof` `(prime));` ` ` `// Only 2, 3, 5 and 7 are prime` ` ` `// one-digit number` ` ` `prime[2] = prime[3] = ` `true` `;` ` ` `prime[5] = prime[7] = ` `true` `;` ` ` `int` `temp = n, count = 0;` ` ` ` ` `// Loop to compute all the digits` ` ` `// of the number untill it` ` ` `// is not equal to the zero` ` ` `while` `(temp != 0) {` ` ` `// Fetching each digit` ` ` `// of the number` ` ` `int` `d = temp % 10;` ` ` `temp /= 10;` ` ` `// Checking if digit is greater than 0` ` ` `// and can divides n and is prime too` ` ` `if` `(d > 0 && n % d == 0 && prime[d])` ` ` `count++;` ` ` `}` ` ` `return` `count;` `}` `// Driven Code` `int` `main()` `{` ` ` `int` `n = 1032;` ` ` `cout << countDigit(n) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to count number of digits` `// which is prime and also divides number` `class` `GFG {` ` ` ` ` `// Function to find the number of` ` ` `// digits in number which divides the` ` ` `// number and is also a prime number` ` ` `static` `int` `countDigit(` `int` `n)` ` ` `{` ` ` `boolean` `prime[] = ` `new` `boolean` `[` `10` `];` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < ` `10` `; i++)` ` ` `prime[i] = ` `false` `;` ` ` `// Only 2, 3, 5 and 7 are prime` ` ` `// one-digit number` ` ` `prime[` `2` `] = prime[` `3` `] = ` `true` `;` ` ` `prime[` `5` `] = prime[` `7` `] = ` `true` `;` ` ` ` ` `int` `temp = n, count = ` `0` `;` ` ` ` ` `// Loop to compute all the digits` ` ` `// of the number untill it` ` ` `// is not equal to the zero` ` ` `while` `(temp != ` `0` `) {` ` ` ` ` `// Fetching each digit` ` ` `// of the number` ` ` `int` `d = temp % ` `10` `;` ` ` ` ` `temp /= ` `10` `;` ` ` ` ` `// Checking if digit is greater than 0` ` ` `// and can divides n and is prime too` ` ` `if` `(d > ` `0` `&& n % d == ` `0` `&& prime[d] == ` `true` `)` ` ` `count++;` ` ` `}` ` ` ` ` `return` `count;` ` ` `}` ` ` ` ` `// Driven Code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `1032` `;` ` ` ` ` `System.out.println(countDigit(n)) ;` ` ` `}` `}` `// This code is contributed by Yash_R` |

## Python3

`# Python program to count number of digits` `# which is prime and also divides number` `# Function to find the number of` `# digits in number which divides the` `# number and is also a prime number` `def` `countDigit(n):` ` ` `prime ` `=` `[` `False` `]` `*` `10` ` ` `# Only 2, 3, 5 and 7 are prime` ` ` `# one-digit number` ` ` `prime[` `2` `] ` `=` `True` ` ` `prime[` `3` `] ` `=` `True` `;` ` ` `prime[` `5` `] ` `=` `True` ` ` `prime[` `7` `] ` `=` `True` `;` ` ` `temp ` `=` `n` ` ` `count ` `=` `0` `;` ` ` ` ` `# Loop to compute all the digits` ` ` `# of the number untill it` ` ` `# is not equal to the zero` ` ` `while` `(temp !` `=` `0` `):` ` ` ` ` `# Fetching each digit` ` ` `# of the number` ` ` `d ` `=` `temp ` `%` `10` `;` ` ` `temp ` `/` `/` `=` `10` `;` ` ` `# Checking if digit is greater than 0` ` ` `# and can divides n and is prime too` ` ` `if` `(d > ` `0` `and` `n ` `%` `d ` `=` `=` `0` `and` `prime[d]):` ` ` `count ` `+` `=` `1` ` ` `return` `count` `# Driver Code` `n ` `=` `1032` `print` `(countDigit(n))` `# This code is contributed by ANKITKUMAR34` |

## C#

`// C# program to count number of digits` `// which is prime and also divides number` `using` `System;` `class` `GFG {` ` ` ` ` `// Function to find the number of` ` ` `// digits in number which divides the` ` ` `// number and is also a prime number` ` ` `static` `int` `countDigit(` `int` `n)` ` ` `{` ` ` `bool` `[]prime = ` `new` `bool` `[10];` ` ` ` ` `for` `(` `int` `i = 0; i < 10; i++)` ` ` `prime[i] = ` `false` `;` ` ` `// Only 2, 3, 5 and 7 are prime` ` ` `// one-digit number` ` ` `prime[2] = prime[3] = ` `true` `;` ` ` `prime[5] = prime[7] = ` `true` `;` ` ` ` ` `int` `temp = n, count = 0;` ` ` ` ` `// Loop to compute all the digits` ` ` `// of the number untill it` ` ` `// is not equal to the zero` ` ` `while` `(temp != 0) {` ` ` ` ` `// Fetching each digit` ` ` `// of the number` ` ` `int` `d = temp % 10;` ` ` ` ` `temp /= 10;` ` ` ` ` `// Checking if digit is greater than 0` ` ` `// and can divides n and is prime too` ` ` `if` `(d > 0 && n % d == 0 && prime[d] == ` `true` `)` ` ` `count++;` ` ` `}` ` ` ` ` `return` `count;` ` ` `}` ` ` ` ` `// Driven Code` ` ` `public` `static` `void` `Main (` `string` `[] args)` ` ` `{` ` ` `int` `n = 1032;` ` ` ` ` `Console.WriteLine(countDigit(n)) ;` ` ` `}` `}` `// This code is contributed by Yash_R` |

## Javascript

`<script>` `// Javascript program to count number of digits` `// which is prime and also divides number` `// Function to find the number of` `// digits in number which divides the` `// number and is also a prime number` `function` `countDigit(n)` `{` ` ` `var` `prime = Array(10).fill(` `false` `);` ` ` `// Only 2, 3, 5 and 7 are prime` ` ` `// one-digit number` ` ` `prime[2] = prime[3] = ` `true` `;` ` ` `prime[5] = prime[7] = ` `true` `;` ` ` `var` `temp = n, count = 0;` ` ` ` ` `// Loop to compute all the digits` ` ` `// of the number untill it` ` ` `// is not equal to the zero` ` ` `while` `(temp != 0) {` ` ` `// Fetching each digit` ` ` `// of the number` ` ` `var` `d = temp % 10;` ` ` `temp = parseInt(temp/10);` ` ` `// Checking if digit is greater than 0` ` ` `// and can divides n and is prime too` ` ` `if` `(d > 0 && n % d == 0 && prime[d])` ` ` `count++;` ` ` `}` ` ` `return` `count;` `}` `// Driven Code` ` ` `n = 1032;` ` ` `document.write(countDigit(n));` `</script>` |

**Output:**

2

Time Complexity: O(log_{10}n)

Auxiliary Space: O(prime)