Question

Show that 12n cannot end with the digit 0 or 5 for any natural number n.

NCERT Class X
Mathematics - Exemplar Problems

Chapter _Real Numbers

Answer 1

12n can only end with digits 0 or 5 when it base prime factors include 2 and 5 as its factors.

but 12 has not 2 and 5 as its prime factors . so it is impossible for 12n to end with the digit 0 or 5

Answer 2

a=bq+r

n=0,1

12^n = (2*2*3)^n                          

=2(1*1*3)^0

= 2   therefore it ends with 2

=2(1*1*3)^1

=2*2*3

=12   therefore ends with 12

=2(1*1*3)^2

=2*9

=18   therefore ends with 18

therefore 12^n cannot end with 0 or 5

this is how its done im not sure at all