How can I multiply really big numbers c++

The result overflows the int (and also std::uint64_t)

You have to use some BigInt library.

As Jarod42 suggested is perfectly okay, but i am not sure whether overflow will take place or not ?

Try to store each and every digit of number in an array and after that multiply. You will definitely get the correct answer.

For more detail how to multiply using array follow this post http://discuss.codechef.com/questions/7349/computing-factorials-of-a-huge-number-in-cc-a-tutorial

ints only hold 32 bits. When the result of a multiplication is larger than 2^31 - 1, the result rolls over to a large negative value. Instead of using the int data type, use long long int, which holds 64 bits.