Question

show that 12^n never ends with unit digit zero.
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Answer 1

because it will not end with 2power n and 5 power n so it will not end with zero

Answer 2

if the number 12n ,for any n were to end with digit zero then it would be divisible by 5 and 2. that is , the prime factorisation of 12n would contain the prime 5 .this is not possible because 12n contain only 2 and 3 as factors that's why it will never end with unit digit zero