What makes quantum computers good at factoring large numbers is their ability to solve the order finding problem (and a mathematical fact that relates finding prime factors to period finding). That's basically Shor's algorithm in a nutshell. Yet it only begs the question what makes quantum computers good at period finding.

At the core of period finding is the ability to calculate a function's value over its entire domain (that is, for every conceivable input). This is called quantum parallelism. This in itself is not good enough, but together with interference (the ability to combine results from quantum parallelism in a certain way), it is.

I suppose this answer might be a bit of a cliff hanger: How does one use these abilities to actually factor? Find the answer to that at wikipedia on Shor's algorithm.

What makes quantum computers good at factoring large numbers is their ability to solve the period finding problem (and a mathematical fact that relates finding prime factors to period finding). That's basically Shor's algorithm in a nutshell. Yet it only begs the question what makes quantum computers good at period finding.

At the core of period finding is the ability to calculate a function's value over its entire domain (that is, for every conceivable input). This is called quantum parallelism. This in itself is not good enough, but together with interference (the ability to combine results from quantum parallelism in a certain way), it is.

I suppose this answer might be a bit of a cliff hanger: How does one use these abilities to actually factor? Find the answer to that at wikipedia on Shor's algorithm.