Question

Show that the number of the form 7^n, n ∈ N cannot have unit digit zero.

Answer 1

If 7ⁿ has to end with the digit 0 for any natural number n,

then it has to be divisible by 10.

ie. its prime factorisation should have the factors of both 2 and 5 [ since 10=2x5 ]

But we know that 7=7x1

By the fundamental theorem of arithmetics, we also know that there exist no other factors for 7.

Thus we conclude that 7ⁿ cannot end with the digit 0 for any natural number n.