# Ex.1.2 Q5 Real Numbers Solution - NCERT Maths Class 10

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## Question

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

Video Solution
Real Numbers
Ex 1.2 | Question 5

## Text Solution

What is unknown?

Whether $$6^n$$ can end with the digit $$0$$ for any natural number $$n$$.

Reasoning:

If any number ends with the digit $$0$$ that means it should be divisible by $$5$$. That is, if $$6^n$$ ends with the digit $$0$$, then the prime factorization of $$6^n$$ would contain the prime $$5$$.

Steps:

Prime factors of $${6^{{n}}} = {\left( {2 \times 3} \right)^{{n}}} = {\left( 2 \right)^{{n}}}{\left( 3 \right)^{{n}}}$$

You can observe clearly, $$5$$ is not in the prime factors of $$6^n$$.

That means $$6^n$$ will not be divisible by $$5.$$

Therefore, $$6^n$$ cannot end with the digit $$0$$ for any natural number $$n$$.

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