Question

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

Answer 1

We know that the expansion of a^n must be divisible by 2 , 5 to have a zero at the end.

Let's consider 14^n has a zero for some value of n.

So, 14 must be having 2 ,5 in its factorisation.

14 = 2 * 7 . There is no 5 in its factors.

So for all values of n, 14^n can never end with ' 0'

Answer 2

14^n is a natural no. as we know that 14^n has factor with ( 7 * 2 ) .

hence, it does not have factor of (2,5)