A mathematician has an enormous cake and many friends with whom to share it.

First, she gives a quarter of the cake to the first friend.

She then gives a fifth of the remaining cake to the next friend. She then gives a sixth of the now remaining cake to the next friend. This process continues until she gives a hundredth of the remaining cake to the last friend.

She finally takes the portion that is left over for herself.

What percentage of the original cake does she have?