3. Check whether 6" can end with the digit 0 for any natural number n.

1.	3. Check whether 6" can end with the digit 0 for any natural number n.
Answer» If any number ends with the digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as 10 = 2 × 5 Prime factorisation of 6n=(2 ×3)n It can be observed that 5 is not in the prime factorisation of 6n. Hence, for any value ofn, 6nwill not be divisible by 5. Therefore, 6ncannot end with the digit 0 for any natural numbern.

Answer»

If any number ends with the digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as 10 = 2 × 5

Prime factorisation of 6n=(2 ×3)n

It can be observed that 5 is not in the prime factorisation of 6n.

Hence, for any value ofn, 6nwill not be divisible by 5.

Therefore, 6ncannot end with the digit 0 for any natural numbern.

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