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Question
Show that 12n cannot end with the digit 0 or 5 for any natural number n.
Solution
If any number ends with the digit 0 or 5, it is always divisible by 5.
If 12n ends with the digit zero or five it must be divisible by 5.
This is possible only if prime factorisation of 12n contains the prime number 5.
Now, 12 = 2 × 2 × 3 = 22 × 3
12n = (22 × 3)n = 22n × 3n
Since, there is no term containing 5.
Hence, there is no value of n ∈ N for which 12n ends with the digit zero or five.
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