Question

Show that 9n never end with digit 0 for any natural number n

Answer 1

9ⁿ cannot end with digit 0.

If a number [aⁿ] need to end with a digit 0 , it should have it's factors as 5 and 2.

But 9 in 9ⁿ has factors as 3² ,i.e., only 3 as factor .

So according to the fundamental theorem of arithmetic 9ⁿ cannot end with digit 0.

Answer 2

9n can never end with the digit 0 for any natural number n because for a number to end with zero it should be divisible by 10 and therefore its factors should be 5 and 2.

But as 9 has only 3 as its factor, increasing its power will not make 5 as its factor.

Thus it can never end with 0.