Question

How many positive, integers
N give a remainder 8 when
2008 is divided by N​

Answer 1

Answer:

f 'n' when divided by 8 leaves a remainder 5, then 'n' can be written in the form: (8k + 5), where k is a natural number.

Note: Divison Algorithm

[Dividend = Divisor*Quotient + Remainder]

So n = 8k+5

or, 2n+4 = 2*(8k+5) + 4 = 16k+14

So, R[(2n+4)/8]

= R[(16k+14)/8]

= R[(16k)/8] + R[(14)/8]

= 0 + 6

= 6 (Answer)

Alternate Method:

This is a generic question . So, we can assume a value of n which satisfies the condition.(True for one, True for all)

Let n = 13

So, (2n + 4) = 30

R[(2n+4)/8] = R(30/8) = 6 (Answer)

Explanation:

Answer 2

Answer:

f 'n' when divided by 8 leaves a remainder 5 then 'n ' can be written in the form : (8k+5) , where k is a natural number

note : division algorithm

[dividend=divisor*question + remainder]

so n=8k+5

or 2n+4=2*( 8k+5 )+4=16k+14

so, R [2n+4/8]

R [(16k+14)/8]

=6( answer )

Explanation:

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