Question

By what quantity must the heat capacity be divided to obtain the specific heat of that material

Answer 1

Heat capacity of an object, is the amount of heat energy or thermal energy (unit: Joule) needed to raise the temperature of the object by 1 degree celsius. Unit of heat capacity is J/°C 

Larger object will surely need larger amount of thermal energy to raise its temperature. If you compare 1 litre of water with 0.5 litre of water, the 1L water will have two times the heat capacity. 

It will be more useful to compare specific heat capacity, because then it is the amount of heat energy or thermal energy (unit: Joule) needed to raise the temperature of 1 unit mass of the object by 1 degree celsius. You can then compare between 1 unit mass of water and 1 unit mass of iron. 
Water has higher specific heat capacity than iron, meaning that you need more energy to heat up 1kg of water, then to heat up 1kg of iron. 

The unit will then be J/(kg °C) or J/(g °C).