The Quadrantid meteor shower is among the strongest annual meteor showers, and has drawn the attention of scientists for several decades. The stream is unusual, among others, for several reasons: its very short duration around maximum activity (~12 - 14 hours) as detected by visual, photographic and radar observations, its recent onset (around 1835 AD) and because it had been the only major stream without an obvious parent body until 2003. Ever since, there have been debates as to the age of the stream and the nature of its proposed parent body, asteroid 2003 EH1. In this work, we present results on the most probable age and formation mechanism of the narrow portion of the Quadrantid meteoroid stream. For the first time we use data on eight high precision photographic Quadrantids, equivalent to gram - kilogram size, to constrain the most likely age of the core of the stream. Out of eight high-precision photographic Quadrantids, five pertain directly to the narrow portion of the stream. In addition, we also use data on five high-precision radar Quadrantids, observed within the peak of the shower. We performed backwards numerical integrations of the equations of motion of a large number of clones of both, the eight high-precision photographic and five radar Quadrantid meteors, along with the proposed parent body, 2003 EH1. According to our results, from the backward integrations, the most likely age of the narrow structure of the Quadrantids is between 200 - 300 years. These presumed ejection epochs, corresponding to 1700 - 1800 AD, are then used for forward integrations of large numbers of hypothetical meteoroids, ejected from the parent 2003 EH$_1$, until the present epoch. The aim is to constrain whether the core of the Quadrantid meteoroid stream is consistent with a previously proposed relatively young age (~ 200 years).}