Which does John like

Factors of numbers he likes:
400 = 2 2 2 2 5 5;
100 = 2 2 5 5;
2500 = 2 2 5 5 5 5;


Dislikes:
300 =3 5 5;
99 = 3 3 11;
2400 = 2 2 2 2 2 3 5 5.

The numbers he likes are all perfect squares and are only made up of 2's and 5's. Based on the given information there are two logical answers:

Actually, he likes 3600 which is 2 2 2 2 3 3 5 5, so he doesn't seem to be particular about the factors.

He likes squares. 900 is the answer.

Try again, sent you a PM

My conclusion agrees with mark.

John likes numbers that have nice round square roots

400 sq r. 20
100 sq r. 10
3600 sq r. 60
900 sq r. 30

all the others give a number followed by .756348484 or similar.

900 it's a square