Mathematics · Real Numbers · NCERT Examples

Example 1

A complete, independently verified solution for NCERT Example 1.

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Mathematics · Chapter 1 · NCERT Examples

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NCERT Example

Example 1

prime factorisation · terminal digit

Consider the numbers 4ⁿ, where n is a natural number. Check whether there is any value of n for which 4ⁿ ends with the digit zero.

Solution

4^n=(2^2)^n=2^{2n}

A number ending in zero is divisible by 10 = 2 × 5, so its prime factorisation contains both 2 and 5. The factorisation of 4ⁿ contains only 2 and has no factor 5.

Final answer

There is no natural number n for which 4ⁿ ends with zero.