For what value of - n - would 4n end with zero-A- It will not end with zero for any value of n -B- 10C- 0D- Can-t say

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Standard X

Mathematics

Fundamental Theorem of Arithmetic

For what valu...

Question

For what value of ‘n’ would $4^{n}$ end with zero?

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It will not end with zero for any value of n.

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Can’t say

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Solution

The correct option is C
It will not end with zero for any value of n.

$4^{n} = 2^{2 n}$
Now, if a number ends with zero, it should be divisible by 5.
$\Rightarrow$ One of the prime factors will be 5.
But $4^{n}$ is not divisible by 5, therefore it will never end with zero.

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For what value of ‘n’ would 4n end with zero?

The correct option is C It will not end with zero for any value of n. 4n=22n Now, if a number ends with zero, it should be divisible by 5. ⇒ One of the prime factors will be 5. But 4n is not divisible by 5, therefore it will never end with zero.

For what value of ‘n’ would $4^{n}$ end with zero?

The correct option is C
It will not end with zero for any value of n.

$4^{n} = 2^{2 n}$
Now, if a number ends with zero, it should be divisible by 5.
$\Rightarrow$ One of the prime factors will be 5.
But $4^{n}$ is not divisible by 5, therefore it will never end with zero.