CBSE Class 10 Answered
CHECK WHETHER 6 raise to n can end with me digit zero for any natural number n
Asked by rushi chincholkar | 01 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 | 01 Jun, 2013, 10:16: PM
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