Question

check whether 4n can end with the digit 0 for any natural number n

Answer 1

is the number 4n for any n were to end with digit zero then it would be divisible by 5 and 2 . that is the prime factorization of 4n contain the prime 5 and 2 this is not possible because 4n=(2)^2n so the only prime in the factorization of 4n is 2 So the uniqueness of the fundamental theorem of arithmetic guarantee that there are no other prime in the factorization of 4n So there is no natural no n for which 4n ends with the digit zero.

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