Around 3.2k HP to be safe. People have done it with less though and he does around 11k touch damage. Only have to watch out for magic damage if your buying which is around 3.2k
The suggested 3200 HP is what people usually recommend to safely take any hit (including powered up) from Zakum, as his attacks usually peak at around 3100 damage. So to answer your question, you need 2000 HP before HB (3200 / (1.6) = 2000)