This site explains how to calculate in your head (in often less than one second) the day of the week for any calendar date. It also explains how to calculate the day, month or year when one of those other elements of a date is unknown but the day of the week is known. There is no faster or simpler formula out there.
The number 7 is important in the DOW formula because the weekly calendar repeats itself every 7 days. So what are the multiples of 7, starting with 0 and ending with 35