A method for determining p - adic orders of factorials

In this paper,with a prime p the p - adic size of n! where n is a positive integer is determined for ordp n = 0 and ordp n > 0. the discussion begins with the determination of the p - adic sizes of factorial functions pα!,qα! and (pα qβ)! with α,β > 0 and q a prime different from p. it is found that ord ppp! = pα - 1/p - 1 with α > 0. results are then used to obtain the explicit form of p - adic sizes of n from works of earlier authors. it is also found that the p - adic orders of ncr = n!/(n-r)!r! is given by where n = pα and r = pθ with α > θ > 0.