Question

Show that 17 n cannot end with digit 0 and 5

Answer 1

Answer:

If any number ends with the digit 0 or 5, it is always divisible by 5. If 17n ends with the digit zero it must be divisible by 5. This is possible only if prime factorisation of 17n contains the prime number 5.

17 = 1 × 17 × ⇒ 17n = (1 × 17)n = n × 17n

Since its prime factorisation does not contain 5.

Hence, 17n cannot end with the digit 0 or 5 for any natural number n.

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