Question

show that 6n cannot end with the digit 0 for any natural number

Answer 1

6n can end with 0, the must have 2 and 5 as it prime factors .
      6=2x3
      6n=(2x3)n
      6n=2nx3n
since it has no 5 as its prime factor.
therefore 6n cannot end with 0

Answer 2

Answer:

Step-by-step explanation: if number 6n, for any valie of n were to end with the digit 0,then it would be divisible by 5.That is, the prime factorisation of 6n would contain the prime no. 5.This is not possible because 6n=(2×3)n, so the primes in the factorisation of 6n are 2and3.so the uniqueness of the fundamental theorem of arithmatic guarantees that there are no other primes in factorisation of 6n.so, there is no natural no. n for which 6n ends with the digit 0.

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