I think throughout the series, J.K. Rowling used a lot of symbolism through numbers. For example, the Deathly Hallows are three objects that are extremely important in Wizard lore--one might even call them holy. Could this be an allusion to another holy trio? And what about the horcruxes? Voldemort planned on splitting his soul into seven, which is known as a lucky or magical number. When he killed the Potters, he unknowingly created an extra horcrux (Harry). So, in the end, his soul was split into eight pieces. However, only seven ever existed at any one time. There's also seven years of Hogwarts, seven books, and seven is the age when a child should show magical talent (says Rita Skeeter). In Jewish culture, seven symbolizes human existence--the days of work and the day of rest combined into one week. Eight symbolizes going beyond what's human, beyond a physical existence--like the eighth day of the week (which doesn't physically exist).
I think J.K. Rowling is trying to say that when Voldemort split his soul another time, he was no longer human, no longer truly existing as a person. He wasn't technically possible, yet still real and living. If you think about it mathematically, splitting his soul in half left him with half a soul, then a fourth, and so on, leaving him with 1/128th of a soul. That's not even one percent of a soul--dangerously close to being soulless, like being kissed by a dementor.
Many could argue this is a coincidence, but J.K. Rowling planned a series with seven books. Not five, not three, but seven. I think this was a significant and conscious decision. Especially with the success of the books, you'd think Rowling might have chosen to write more about Harry and his friends. But through everything, she stuck to a trusty set of seven.
What other numbers are symbolic in HP7? Where else is the number seven mentioned? Do seven and eight have other meanings in culture? Tell me what you think!