Question

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

Answer 1

$\huge\boxed{\fcolorbox{white}{pink}{Answer}}$

If the number 6n ends with the digit zero (0),

then it should be divisible by 5,

as we know any number with unit place as 0 or 5 is divisible by 5.

Prime factorization of 6^n = (2×3)^n

Therefore,

the prime factorization of  doesn’t contain prime number 5.

Hence, it is clear that for any natural number n,

6n is not divisible by 5 and thus it proves that cannot end with the digit 0 for any natural number n.

Answer 2

Question:-

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

✨$\huge\mathcal\color{olive} AnSwEr::$

➣ If the number 6n ends with the digit zero (0),

then it should be divisible by 5,

as we know any number with unit place as 0 or 5 is divisible by 5.

Prime factorization of 6^n = (2×3)^n

Therefore,

the prime factorization of doesn’t contain prime number 5.

Hence, it is clear that for any natural number n,

6n is not divisible by 5 and thus it proves that cannot end with the digit 0 for any natural number n.

$\huge\mathcal\color{green}Hence \ Proved$

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