Question

Show that a number 7^n cannot end with digit 0 for every natural number n​

Answer 1

Answer:

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. 

hope it will help u

Answer 2

Answer:

To end with 0 , any positive no. should have 2 and 5 has a factor I.e.

N(To end with 0) = 2^n × 5^n

So in the above question

7^n

There is neither involvement of 2 nor 5

So 7^n cant end with digit 0 for every natural no. n...