can 5 raise to the power n can end with 0 for any natural number

Asked by vikramsingh | 27th May, 2013, 01:37: PM

Expert Answer:

If any number ends with the digit 0, it should be divisible by 10 or in other words its prime factorisation must include primes 2 and 5 both.

Prime factorisation of 5n = 5n , which does not include 2.

Also, by Fundamental Theorem of Arithmetic Prime factorisation of a number is unique. So 2 is not a prime factor of 5n.

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

Answered by  | 27th May, 2013, 03:48: PM

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