# 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 = 12
Output: 1
Explanation:
Digits of the number = {1, 2}
But, only 2 is prime number that divides N.

Input: N = 1032
Output: 2
Explanation:
Digits of the number = {1, 0, 3, 2}
3 and 2 divides the number and are also prime.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 implementation of this approach:

## C++

 `// C++ program to count number of digits ` `// which is prime and also divides number ` ` `  `#include ` ` `  `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; ` `    ``memset``(prime, ``false``, ``sizeof``(prime)); ` ` `  `    ``// Only 2, 3, 5 and 7 are prime  ` `    ``// one-digit number ` `    ``prime = prime = ``true``; ` `    ``prime = prime = ``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``; ` `         `  `        ``for` `(``int` `i = 0; i < 10; i++) ` `            ``prime[i] = ``false``; ` ` `  `        ``// Only 2, 3, 5 and 7 are prime  ` `        ``// one-digit number ` `        ``prime = prime = ``true``; ` `        ``prime = prime = ``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 `

Output:

```2
```

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : ANKITKUMAR34, Yash_R