Dividing numbers by constants without dividers?

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The concept is this:

suppose your input is x, coeff is y and you choose 14 bits resolution:

c = c * 2^n/2^n;

c = round(c*2^n)/2^n;

the term round(c*2^n) you precompute it, call it y, then in design you multiply:

x * y gives result, divide by 2^n i.e. discard n bits with/without rounding

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Thank you for your prompt reply. I am trying to understand that but I might be missing something...

So if x = 150, c = 3 and n = 3 then y = 3*2^3 = 24 -> 150*24 = 3600 and if I shift that n positions then I get 450 when I should get something near 150/3 = 50. What did i get wrong?

Edit: the result is nearly correct if I shift 2*n positions. Does it mean anything?