Question

using fundamental theorem of arithmetic check whether there is any value of n for which 5^n ends with the digit zero.

Answer 1

for any positive integer ending with the digit 0 is divisible by 5. so its prime factorization must contain Prime 5 but we have 5^n=5 it has only prime factor is 5 and to does not occur in this prime factorization therefore 5 ^n does not end with a digit 0 for any natural number n.

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