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show that 12n cannot end with digit 0 or 5 for any natural number n

Here, Number=12n where n stand for any natural number .

Now 12n= (22 x3)n

Now , For 12n to end with 0, it should have 2 as well as 5 in its Prime factors to end with 0, Also to end with 5 , it requires at least a single multiple of 5 in its Prime Factors, So 12n cannot end with the digit 0 or 5.

Hope it helps!!

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12n will end with 0 if 5 is one of the prime fctors of 12
but this is not possible as 12=2*2*3
where 5 is not there
hence 12ncouldn't end with 0

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By the law that a number can be expressed as the powers of its factors.

Therefore, any number ending with 0 or 5 must have its factors as 2n * 5n as 0 as unit digit is only possible by the interactions of powers of 2&5.

Since factors of 12 are 2 and 3. There is no 5 as factor.

Therefore 12n can't end with 0 or 5.

Cheers!! hope it helps

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