Question

Show that any number of the form 6raise to x,XEN can never end with digit zero .

Answer 1

The prime factorisation of 6^x

= (2×3)^x

So it does contain a 2 in its prime factorisation but in this case a 5 is missing .

That means that it is not divisible by 2×5 both i.e. 10, So it is not possible for the number to end with a zero if its not divisible by 10.

This is the simple way to state that “ for any real number to end with zero its prime factorisation must contain 2×5 in it.”

So in your case the number 6^x will never end with zero for any natural value of 10