About gross domestic product at factor cost GDP at factor cost= Net value added + Depreciation. Here my question is why depreciation added to Net value added? I am confused here: Net value added = Gross value added - depreciation; so the above formula becomes GDP at factor cost= Gross value added - depreciation + Depreciation. Here depreciation get cancelled and finally becomes GDP at factor cost= Gross value added.
Source: http://www.economicsdiscussion.net/national-income/components-national-income/top-17-components-of-national-income/18793
The best practice would be to use definitions from recognized international institutions such as the World Bank or the Organisation for Economic Co-operation and Development (OECD). In this document The OECD classifies three types of gross value added (1) at  basic  prices, (2) at producers' prices and (3) at factor cost. 

Let first define gross value added at  basic  prices  as  output  valued  at  basic  prices  less  intermediate consumption valued at purchasers' prices. Then, gross  value  added at  factor  cost  can  be  derived  from  gross  value  added  at  basic  prices  by subtracting other taxes less subsidies on production. 

As an example, GDP  at  market  prices  for  the  United  States  in  1992  was US\$ 6,234 billion.  As GDP at factor cost removes all net taxes on production, it would equal \$6,234 billion less \$506 billion or \$5,728 billion.

GDP at factor cost is thus a way of measuring gross value added at some prices. So, as far as I understand, it makes sense that depreciation get cancelled and finally becomes GDP (at factor cost) = Gross value added (at factor cost).

Why is depreciation added to Net value added? According to your source, if we deduct depreciation from Gross Net Product (at factor cost), we get Net National Product (at factor cost). So, if we add depreciation to NNP we get GNP.