# C Exercises: Check if a given integer is a power of three

## C Programming Mathematics: Exercise-13 with Solution

Write a C program to check if a given integer is a power of three.

Example:

Input: 9

Output: true

Input: 81

Output: true

Input: 45

Output: false

**Visual Presentation:**

**Sample Solution:**

**C Code:**

```
#include <stdio.h>
#include <stdbool.h>
// Function to check if a number is a power of three
static bool is_PowerOf_Three(int n) {
#if 0 // Alternative approach using recursive function
if (n == 1) return true; // Base case: If n is 1, it is a power of three
if (n == 0 || n % 3) return false; // If n is not divisible by 3 or is 0, it is not a power of three
return is_PowerOf_Three(n / 3); // Recursively check if n divided by 3 is a power of three
#else // Optimized approach using mathematical property
return (n > 0 && (1162261467 % n) == 0); // Return true if n is greater than 0 and 1162261467 is divisible by n
#endif
}
// Main function to test the is_PowerOf_Three function with different numbers
int main(void) {
int n = 9;
printf("\nIf %d is a power of three? %d", n, is_PowerOf_Three(n));
n = 81;
printf("\n\nIf %d is a power of three? %d", n, is_PowerOf_Three(n));
n = 45;
printf("\n\nIf %d is a power of three? %d", n, is_PowerOf_Three(n));
return 0;
}
```

Sample Output:

If 9 is power of three? 1 If 81 is power of three? 1 If 45 is power of three? 0

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