Question

Show that 12 ki power n cannot end with the0 or 5 digit for any natural no.n

Answer 1

Solution :

If 12^n end with 0 then, for some natural number n, is divisible by 5.

•°• Prime factorisation of 12^n contains the prime 5.

Let's

$\tt12 \longrightarrow2 \times 2 \times 3.$

But, here prime factorisation of 12 is not 5.

so,

It is not possible12^n end with 0, according to Fundamental theorem of Arithmetic, the prime factorisation.