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    <p>Ok, this is my take on it. Hope it might be of use (EDIT: not to provoke "don't use leading underscore" comments - added a namespace). EDIT #2: Added a faster function <code>get_factor_prime_faster()</code> with a helper function. See notes about the speed tests in the end. </p> <pre><code>#include &lt;cstdint&gt; #include &lt;iostream&gt; namespace so { // Head-on approach: get_factor_prime() std::uint64_t get_factor_prime( std::uint64_t _number ) { for( std::uint64_t i_ = 2; i_ * i_ &lt;= _number; ++i_ ) if( _number % i_ == 0 ) return ( get_factor_prime( _number / i_ ) ); return ( _number ); } // Slightly improved approach: get_factor_prime_faster() and detail::get_factor_prime_odd() namespace detail { std::uint64_t get_factor_prime_odd( std::uint64_t _number ) { for( std::uint64_t i_ = 3; i_ * i_ &lt;= _number; i_ += 2 ) if( _number % i_ == 0 ) return ( get_factor_prime_odd( _number / i_ ) ); return ( _number ); } } // namespace so::detail std::uint64_t get_factor_prime_faster( std::uint64_t _number ) { while( _number % 2 == 0 ) _number /= 2; return ( detail::get_factor_prime_odd( _number ) ); } } // namespace so int main() { std::cout &lt;&lt; so::get_factor_prime( 600851475143 ) &lt;&lt; std::endl; std::cout &lt;&lt; so::get_factor_prime( 13195 ) &lt;&lt; std::endl; std::cout &lt;&lt; so::get_factor_prime( 101 ) &lt;&lt; std::endl; std::cout &lt;&lt; so::get_factor_prime_faster( 600851475143 ) &lt;&lt; std::endl; std::cout &lt;&lt; so::get_factor_prime_faster( 13195 ) &lt;&lt; std::endl; std::cout &lt;&lt; so::get_factor_prime_faster( 101 ) &lt;&lt; std::endl; return( 0 ); } </code></pre> <p>Program output:</p> <pre><code>6857 29 101 6857 29 101 </code></pre> <p>Admittedly, I still cannot figure out how to check easily if a number is a prime...</p> <p>EDIT: Tested in a loop for <code>600851475143 * 1024</code> number, GCC 4.7.2 with -O3, Linux, Intel i5 Core. Times are as follows (approximately):</p> <p><code>get_factor_prime</code> is <code>3</code> times faster than OP's solution;</p> <p><code>get_factor_prime_faster</code> is <code>6</code> times faster than OP's solution.</p>
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