#### Largest Power

```/**
* @file
* @brief Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula.
* @details Given an integer n and a prime number p, the task is to find the largest x such that
* p^x (p raised to power x) divides n! (factorial). This will be done using Legendre's formula:
* x = [n/(p^1)] + [n/(p^2)] + [n/(p^3)] + \ldots + 1
* @see more on https://math.stackexchange.com/questions/141196/highest-power-of-a-prime-p-dividing-n
* @author [uday6670](https://github.com/uday6670)
*/

#include <iostream> /// for std::cin and std::cout
#include <cassert>  /// for assert

/**
* @namespace math
* @brief Mathematical algorithms
*/
namespace math {

/**
* @brief Function to calculate largest power
* @param n number
* @param p prime number
* @returns largest power
*/
uint64_t largestPower(uint32_t n, const uint16_t& p)
{
// Initialize result
int x = 0;

// Calculate result
while (n)
{
n /= p;
x += n;
}
return x;
}

}  // namespace math

/**
* @brief Function for testing largestPower function.
* test cases and assert statement.
* @returns `void`
*/
static void test()
{
uint8_t test_case_1 = math::largestPower(5,2);
assert(test_case_1==3);
std::cout<<"Test 1 Passed!"<<std::endl;

uint16_t test_case_2 = math::largestPower(10,3);
assert(test_case_2==4);
std::cout<<"Test 2 Passed!"<<std::endl;

uint32_t test_case_3 = math::largestPower(25,5);
assert(test_case_3==6);
std::cout<<"Test 3 Passed!"<<std::endl;

uint32_t test_case_4 = math::largestPower(27,2);
assert(test_case_4==23);
std::cout<<"Test 4 Passed!"<<std::endl;

uint16_t test_case_5 = math::largestPower(7,3);
assert(test_case_5==2);
std::cout<<"Test 5 Passed!"<<std::endl;
}

/**
* @brief Main function
* @returns 0 on exit
*/
int main()
{
test(); // execute the tests
return 0;
}
```