Question

if the number 4n is end with the digit 6, n belongs to N,then the value of n is ????​

Answer 1

Answer:

Correct option is

B

No

For the number 4

n

to end with digit zero for any natural number n, it should be divisible by 5. This means that the prime factorisation of 4

n

should contain the prime number 5.But it is not possible because 4

n

=(2)

2n

so 2 is the only prime in the factorisation of 4

n

. Since 5 is not present in the prime factorization, so there is no natural number n for which 4

n

ends with the digit zero.

Answer 2

Value of n is 2n or any any even natural number like 2,4,6,8...

Given:

the number 4n is end with the digit 6, n belongs to N

To find:

Value of n

Solution:

We have to find that power of n such that $4^{n}$ ends with the digit 6.

Ex:-

4² = 4*4 = 16

So, if the value of n is 2, then its last digit will be six.

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

So, the 2n will be factors of natural number

2n means every even number starting 2

So, the value of n is all the even natural numbers.

Ex

4² = 16

$4^{4}$ = 216

$4^{6}$ = 4096

and so on..

Hence, the answer is 2n or any even natural number.

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