In this article we develop a new approach to Clifford Algebras, using the set of natural numbers in base k, for a given number k, none of its digits in this base is zero. This set turns out to be the base of an Algebra over the real numbers and the quotient over one of its two sided ideal conveniently chosen corresponds to the Clifford Algebras. As an addendum, we compute the dimension of the Clifford Algebras.