Show that the number $4^{n}$ , when n is a natural number cannot end with the digit zero

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Solution

If any number ends with zero, then it must be divisible by 5
Hence, its prime factorization must contain 5
But we know,
$4 = 2 \times 2$
So, there is no natural number $n$ for which $4^{n}$ can end with zero

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Consider the number $4^{n}$ , where n is a natural number. Check whether there is any value of n for which $4^{n}$ ends with the digit zero. [2 MARKS]

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Show that the number 4n, when n is a natural number cannot end with the digit zero

If any number ends with zero, then it must be divisible by 5Hence, its prime factorization must contain 5But we know,4=2×2So, there is no natural number n for which 4n can end with zero

Show that the number $4^{n}$ , when n is a natural number cannot end with the digit zero

If any number ends with zero, then it must be divisible by 5
Hence, its prime factorization must contain 5
But we know,
$4 = 2 \times 2$
So, there is no natural number $n$ for which $4^{n}$ can end with zero