Question

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

Answer 1

For a number to be end with digit zero its prime factors must have atleast one 2 and A are 5 both and for a number to be end with 5 its prime factors must have at least one 5.

But in case of (12)^n there is no ’5’ in prime factors of 12 i.e., 12 = 2 x 2 x 3. Hence (12)^n can neither end with zero nor by 5.