p-adic valuation and legendre's formula

 V_p(n) = k => highest power of prime p in number 'n' is k.
This is known as p-adic valuation.
For e.g.
V2(12) = 2
=> p-adic valuation of 2 wrt 12 is 2.
Also it's additive, ie
V_p(m.n) = V_p(m) + V_p(n)
V2(36) = V2(18.2) = V2(18) + V2(2) = 1 + 1 = 2

Legendre's formula:



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