Question

Show that 7n cannot end the digit 0 for any natural number n...

Answer 1

If 7ⁿ ends with a 0 the it must be divisible by 10 i.e., its prime factors should have the factors of both 2 and 5 since 2×5=10.
But, 7ⁿ=(7×1)ⁿ
Therefore by the fundamental theorem of arithmetic (there is no prime factors of 7 other than 7 and 1) we can conclude that 7ⁿ can not end with 0. 

Answer 2

Answer:

according  to fundamental theorem of arithmetic every number should be expressed in the form of 2^n * 5^m .

but 7^n cannot be expressed in the form of 2^n*5^m

therefore 7^n cannot end with zero