A bunny had an infinite number of carrots. A group of bunnies tried to steal those carrots from him. The bunny decided to hide the carrots in a nearby cave. He dug up $100$ holes and labeled them from $1$ to $100$. Then he stored the carrots in the holes labeled as the multiples of $1,2,3,...,50.$

In other words, he stored a carrot in the holes labeled $1,2,3,...,100$. After that he stored a carrot in the holes labeled $2,4,6...100$. Next, he stored them in holes labeled $3,6,9,...,99$. And it went on. When he started storing the carrots in holes labeled as the multiples of $51$, the robbers came and took away all his carrots. How many carrots did he manage to save?

In other words, he stored a carrot in the holes labeled $1,2,3,...,100$. After that he stored a carrot in the holes labeled $2,4,6...100$. Next, he stored them in holes labeled $3,6,9,...,99$. And it went on. When he started storing the carrots in holes labeled as the multiples of $51$, the robbers came and took away all his carrots. How many carrots did he manage to save?

Number Theory