Has knowing those factorisations come in handy?
Not at all. Do you think I would stuff my primitive cerebrum with the mere memorization of identities? But the looking up of them when necessary has been a great help.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.