Question

Show that 12" cannot end with the digit 0 or 5 for any natural number n.
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Answer 1

here your answer dear...

0and 5

0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,0.10

1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,1.10,

2.1,2.2,2.3,2.4,2.5,2.6,2.7,2.e.t.c

Answer 2

here is your ans....

if the number 12n ,for any n ,were to end with the digit 0 or 5 ,then it must be divisible by 5

but here we see that 12 = 2 x 2 x3

then by using the fundamental theorem of arithmetic ,we can say that there is no other prime in in the factorization of 12n

thus there is no n for which the digit 12n were to end with the digit 0 or 5

hope this will help you