Question

Show that a number of the form 14", where n is a natural number can never end with digit
zero.
​

Answer 1

if the number 14^n ,for any n , were to end with the digit zero, then it would be divisible by 5.

the uniqueness of the fundamental theorem of arithmetic guarantees that there are no other prime factors other than 2 and 7 on factorising 14.

so, there is no natural number n for which 14n ends with the digit zero.

Thanks

Mark branliest , please. ..

@ join the army of the shadows

Answer 2

$\huge\underline\mathrm{Question-}$

Show that a number of the form 14", where n is a natural number can never end with digit zero.

$\huge\underline\mathrm{Solution-}$

If any number ends with digit zero, it should be divisible by 10 or in other words, it'd also be divisible by 2 and 5 as 10 = 2 × 5.

Prime factorisation of 14ⁿ = ( 2 × 7 )ⁿ

Here, it can be observed that 5 is absent in the prime factorisation of 14ⁿ, which is a contradiction.

Hence, for any value of n, 14ⁿ will not be divisible by 5.

$\therefore$ 14ⁿ can never be end with zero for any natural number n.

$\rule{100}1$

Similar question's link that I'd answer earlier :

https://brainly.in/question/15008447