Show that the 5'n cannot ends with the digits 2 for natural numbers
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Step-by-step explanation:
As to end with the number 2, we also should have 5^n divisible by 2. That is, the prime factorisation of 5n should contain the number 2. But this is not at all possible as 5^n contains only 5 and 1.
So by the uniqueness of theorem of arithmetic there is no other factor of 5^n other than the 5 and 1 here.
Therefore 5^n cannot end with the digit 2 for any natural number n
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