A farmer is taking her eggs to the market in a cart, but she hits a  pothole, which knocks over all the containers of eggs.  Though she is  unhurt, every egg is broken.
So she goes to her insurance agent, who  asks her how many eggs she had.  She says she doesn’t know, but she  remembers something from various ways she tried packing the eggs.

When she put the eggs in groups of two, three, four, five, and six  there was one egg left over, but when she put them in groups of seven  they ended up in complete groups with no eggs left over.

What can the farmer and agent figure out from this information about the number of  eggs she had ?

Is there more than one answer ?

PS:- Though I know the answer but still I want the answer in the simplest understandable manner possible. Thanks for all answers in advance.

A special integer exists in mathematics that shows a special property.

If you subtract any number from that integer, the result will always be divisible by the successor of that number completely.

Do you know what that integer is ?