Question

Check whether 12n can end with the digit 0 any natural number n​

Answer 1

ANSWER!!:

12n Can't end with the digit zero (0) because for ending with digit zero (0) it is necessary for having the factor 2 and 5 but here the factor is 2 × 2 × 3. so, 12n can't end with the digit zero (0) .

Step-by-step explanation:

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.

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