# 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 \(n\).