jk rowling - Harry Potter: Why 7?

While rereading the entire Harry Potter series I noticed that the number 7 occurs quite often, for instance:

• Seven books


• Seven Horcruxes planned by Tom Riddle



• Seven Weasley kids


• Seven years at Hogwarts


• Seven Harry Potters


• Seven people in a Quidditch team

Did J.K. Rowling ever mention why 7 was so important in Harry Potter?

Answer

Seven is the most powerfully magical number.

“Yes, sir,” said Riddle. “What I don’t understand, though — just out of curiosity — I mean, would one Horcrux be much use? Can you only split your soul once? Wouldn’t it be better, make you stronger, to have your soul in more pieces, I mean, for instance, isn’t seven the most powerfully magical number, wouldn’t seven — ?”

“Merlin’s beard, Tom!” yelped Slughorn. “Seven! Isn’t it bad enough to think of killing one person?"

_{-- HP and the Half-Blood Prince}

As this answer says, seven is considered a magical number in real-life legends and folklore, but here is confirmation that seven has magical significance in-universe.

The magical properties of the number seven were first discovered by the 13th-century Arithmancer Bridget Wenlock:

Wenlock first scribbled down her ground-breaking theorem on the magical properties of the number seven at breakfast one day apparently on the back of an envelope, using her usual invisible ink. She then proceeded to send her cousin a letter, using what she later believed to be the very envelope concealing the theorem.
_{-- Miranda Goshawk's Book of Spells}

This is also confirmed in the Hufflepuff welcome letter at Pottermore:

Bridget Wenlock, the famous thirteenth-century Arithmancer who first discovered the magical properties of the number seven