Home/Class 10/Maths/

Check whether$$6^{n}$$can end with the digit $$0$$ for any natural number $$n$$.
Speed
00:00
03:05

## QuestionMathsClass 10

Check whether$$6^{n}$$can end with the digit $$0$$ for any natural number $$n$$.

See the analysis below.
4.6
4.6

## Solution

If the number$$6^{n}$$ends with the digits zero. Then, it is divisible by $$5$$. Therefore, the prime factorization of$$6^{n}$$contains the prime $$5$$. This is not possible because the only primes in the factorization of$$6^{n}$$are $$2$$ and $$3$$ and the uniqueness of the fundamental theorem of arithmetic guarantees that there are no other prime-in the factorization of$$6^{n}$$.
So, there is no value of $$n$$ in natural numbers for which$$6^{n}$$ends with the digit zero.