Question

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

Answer 1

Answer:

w. k. t

$12^n=(2 \times 2 \times 3)^n\\=2^n \times 2^n \times 3^n$

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.