There is no doubt that in today's society every single person has to work productively to stay competitive. And among all the factors that would help us work productively, having an environment which is free of noise and distractions stands out as the most important one, from my perspective, based on the following reasons:
To begin with, we are facing enormous amount of man-made noises and distractions in this entertainment-oriented information era. Thanks to the rapid development of smart phones and cyber technologies, we are now burdening ourselves more and more with the impulses to check our phones. For example, I can't help checking my friends' status updates or browsing on news websites purposelessly every thirty minutes even when I'm supposed to concentrate on working or spending quality time with my family. And even if you have outstanding self-control, advertisers would try their best to lure you into wasting time on their contents by sending you notifications which are wrapped in the key-words which, based on the analysis on your preferences, you can't resist. Apparently, we are unable to work productively in such distracting environment. So creating an absolutely quiet and distraction-free environment is critical for us to work productively.
What's more, in terms of biology, maximum level of quietness brings in maximum level of concentration, thus making human beings work most productively. For example, when surgeons are conducting operations, they would normally require that all the staff in the operation room stay quiet so they can concentrate on removing tumors from dedicate brains or inserting bridges into fragile hearts. If they had been disturbed by noises or some other distractions, there would have made the wrong cut and cost the lives of patients. Also, it is common sense that you need to stay quiet in libraries so people can study productively. If a quiet environment were less than the most prominent concern, they would have not been so many regulations against loud speakers in libraries. Freeing yourself from noises and distractions is the first step toward productiveness.
To be frank, I'm not saying that other factors are not important to help us work productively. We can also become productive if we are motivated by known rewards or doing something we're interested in. However, thrills and motivations brought by rewards won't last for a long time and its effects fade over time. On the other hand, doing interested things benefit us more in the willingness aspect than productiveness one. People are willing to do whatever they are interested in, but we can't know for sure that they will do it productively. So we can safely draw the conclusion that other factors do contribute to our productiveness level, however, they just don't play a role as important as an environment which is free of noise and distractions.
In a nutshell, we can benefit the most from an environment which is free of noise and distractions, in regard to being productive at work.