I am a 16-digit number and i am odd. My nature is symmetrical with the product of digits as 3374862826400. The sum of all my digits is 104.G

Good suss out, Melody!!!

If one digit appeared 6 times......we would have  to have that digit as a factor 6 times......but we don't, since no single digit factor is repeated more than 5 times.....

What do you mean by symmetrical ?

By symmetrical I am assuming that you mean it is a palindome, BUT

it still does not make sense.

The prime factors of  3374862826400 are  $${{\mathtt{2}}}^{{\mathtt{5}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{5}}}{\mathtt{\,\times\,}}{\mathtt{13}}{\mathtt{\,\times\,}}{\mathtt{9\,613}}{\mathtt{\,\times\,}}{\mathtt{33\,757}}$$

therefore this number can not be the multiple of 16 single digit numbers