The city will begin its affordable housing lottery Monday for 104 apartments at the Williamsburg building that was built at the old Domino Sugar factory site.

Those studios, one-bedrooms and two-bedrooms at 325 Kent Ave. have rents ranging under $1,000 a month for the applicants who fall within the income brackets set by the city’s Department of Housing, Preservation and Development.

Singles who make $21,772 to $25,400 annually are eligible for six studios that rent for $596 while families of four who make between $34,972 and $54,360 can apply for the 13 two-bedrooms that rent for $979 a month.

The rent doesn’t include some of the 16-story building’s amenities such as bike and car parking and a gym.

There will be a preference for lottery applicants who reside within Brooklyn Community Board 1, which covers Williamsburg and Greenpoint, according to HPD.

The remainder of the building’s 418 units will be market rate apartments. It is part of the massive redevelopment of the former 11-acre Domino Sugar factory site, which will bring 2,000 apartments, office space and a green space.

The lottery’s deadline is January 30, 2017 and the building is expected to begin leasing sometime next year. Interested applicants can apply online at nyc.gov/housingconnect or ask for an application by mail at 325 Kent Apts, 243 5th Avenue, Box 425, New York NY 10016.