How does public/private key encryption work, for simpletons?

Blockchains are built on this concept of public/private key (PPK) encryption. How does it work actually?

Fact one: It is easier to multiply 13 and 23 and way faster than it is to figure out what the prime factors of 299 are in your head. Make these numbers much much larger and this fact is still true for computers as well.

Fact two: Using remainders somehow you can use the above fact to create a pair of keys where one will encrypt data and the other will decrypt it, but having one key is only enough to go one way.

Someone fill in the gaps here, cause that's as far as my understanding goes.