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Writing a Number as a Product of Its Primes

Prove 5n. nev...

Question

Prove 5^n.never ends with "0"where "n" is natural number

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Solution

If any number ends with the digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as 10 = 2 × 5

It can be observed that 2 is not in the prime factorisation of 5ⁿ.

Hence, for any value of n, 5ⁿ will not be divisible by 2.

Therefore, 5ⁿ cannot end with the digit 0 for any natural number n.

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