Question

Show that 7^n cannot end with digit zero for any natural number n

Answer 1

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if any number 7^n for any n were to end with the digit 0 then it would be divisible by 5and 2 that is, the prime factorization of 7^n contain the prime 5 and 2. this is not possible because 7 = (7)^n, so the only prime in the factorization of 7 to the power n is 7. show the uniqueness of the fundamental theorem of arithmetic guarantees that there are no other primes in the factorization of 7 to the power n so, there is no natural number and for which 7 to the power n ends with the digit 0

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