Puzzle n°32 (*) - The rows of cups

On the occasion of a cat show, the organizing club wanted to celebrate its jubileum
by offering each cat in competition a silver cup.
The organizers wanted these cups to be all well presented on the podium,
in rows containing each the same number of cups.

They had been trying to put them in 2 rows, then in 3 rows, in 4, 5 or even 6 rows...
But, every single time, they had one cup left !

Finally, they tried to arrange the cups in 7 equal rows, and this was just fine !

How many cups were there at this jubileum show ?
(a cat show typically hosts between 100 and 700 cats)

... I'm giving up ...