prove that every positive integer different from 1 can be expressed as a product of non negative power of 2 and an odd no

let n be a positive integer different from 1 

then it can be expressed as : n= p₁^a1p₂^a2p₃^a3......p_k^ak

there can be 2 different possibilities

1)-    when p1 = 2 and  p₁^a1p₂^a2p₃^a3......p_k^ak are odd positive integers

        n= 2^a1 x  ( p₁^a1p₂^a2p₃^a3...... p_k^ak )

        n = ( a non- negative power of 2) x (an odd positive integer)

2)-   whem each of p₁^a1p₂^a2p₃^a3......p_k^ak are odd positive integers

       n = p₁^a1p₂^a2p₃^a3......p_k^ak

       n = 2⁰ x p₁^a1p₂^a2p₃^a3......p_k^ak

       n =  ( a non- negative power of 2) x (an odd positive integer)