Question

Whether 6
n
can end with digit ′0′ for any natural ′n
'
. Give reason.​

Answer 1

$\large\underline{\sf{Solution-}}$

We know that, any natural number ends with 0 if it contains a factor of 2 and 5.

Now, Prime Factorization of 6 = 2 × 3.

As the prime factorization of 6 don't have any factor of 2 and 5 together, so it never ends with 0.

So, 6^n can never ends with 0 for any n ∈ N.

More to know :-

Fundamental theorem of arithmetic :- This theorem states that Every composite number can be factorized as a product of primes and this prime factorization is unique irrespective of the order of their places.

4 is the smallest composite number.

Answer 2

Step-by-step explanation:

Let us take the example of a number which ends with the digit 0

So, 10= 2×5

100= 2×2×5×5

Here we note that numbers ending with 0 has both 2 and 5 as their prime factors

Whereas 6n = (2×3)n

Does not have 5 as a prime factor.

So, it does not end with zero.

Therefore,6n cannot end with 0 for any natural number n