Question

Show that 12n can't end with '0' or '5' for any natural number 'n'.

Answer 1

Firstly ..assume that 12n ends with 0.....for any natural no. n.
:so,12n is divisible by 5
5 is a prime factor of 12n -equation 1
but 12n=2n×2n×3n
According to uniqueness part of the fundamental theorem of arithmetic only primes involved are 2&3 ....this contradicts that 5 is a prime factor of 12n.
hence our assumption is false...
12n does not end with digit 0...

Hope it helps..!!!