Problem D

Hundred Deck 2

Hundred Deck is a deck consisting of \(100\) cards numbered from \(1\) to \(100\). Each card has the same number printed on both sides. One side of the card is red and the other side of the card is yellow.

Sarai places all of the cards on a table with each cardâ€™s red side facing up. She first flips over every card that has a number on it which is a multiple of \(2\). She then flips over every card that has a number on it which is a multiple of \(3\). Finally, she flips over every card that has a number on it which is a multiple of \(5\).

After Sarai has finished, how many cards have their red side facing up?