Let $$x\textgreater15$$ be the number of students at the bookstore， $$p\textgreater1$$ be the number of pencils each student bought, and $$c\textgreater p$$ be the price of one pencil. We see that $$xcp=1771=7\cdot 11\cdot 23$$. Then we must have $$x=23$$，$$c=11$$，$$p=7$$ by the original conditions and the answer is $$c=11$$． 
2011 AMC10A 10  A majority of the $$30$$ students in Ms. Demeanor\textquotesingle s class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than $$1$$. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was $$$17.71$$. What was the cost of a pencil in cents?  德米诺尔女士班级的 30 个学生中的大多数在学校书店购买铅笔。 这些学生中的每个人都购买了相同数量的铅笔，而且这个数量大于 1。 一支铅笔的成本（以美分计）大于每个学生购买的铅笔数量，所有铅笔的总成本为 $17.71。 一支铅笔的成本是多少？

$$7$$ 
$$11$$ 
$$17$$ 
$$23$$ 
$$77$$ 