A Special Number

Holmes once asked me, “Watson, do you have a preferred number?”

I thought about it for a moment, then answered, “I suppose I rather like three. It has something of a pleasing quality to it.”

Holmes replied with a shake of his head, before proclaiming, “Where is your sense of adventure, Watson? Such a small number, and so little that can be said about it! Now tell me, what do you make of the number 8,549,176,320? It is a rather special one, if you ask me.”

Indeed, it was. But why was it so special?

SOLUTION