CHECK WHETHER 6 raise to n can end with me digit zero for any natural number n

Asked by rushi chincholkar | 1st Jun, 2013, 08:01: PM

Expert Answer:

If the number 6n where n belongs to N, were to end with a zero, then its  prime factorisation  must have 2 and 5 as its  factors.
But 6=2 x 3

6n = (2 x 3)n = 2n x 3n 

So Prime factors of 6n includes only 2 but not 5.

Also from the Fundamental theorem of Arithmetic, the prime factorisation of a number is unique.

Hence a number of the form 6n where n belongs to N, will never end with a zero.

Answered by  | 1st Jun, 2013, 10:16: PM

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