check whether 12n can end with digit 0 for any natural number N
Answers
Answered by
222
w. k. t
12^n=(2 x 2 x 3)^n
=2^n x 2^n x 3^n
If the number 12^n ends with the digit zero, then it is divisible by 5.
Therefore, the prime factorisation of 12^n should contain 5. This is not possible because the prime factorisation of 12 are 2 and 3. So, the uniqueness of Fundamental Theory of Arithmetic guarantees there are no other primes in the factorisation of 12.
Hence,there is no natural number n for which 12^n ends with the digit zero.
Similar questions