Question

a number n when divided by 16 gives the remainder 5 is the remainder when the same number is divided by 8

Answer 1

If a number "n" gives a remainder of 5 when divided by 16, it will give a remainder of 5 when divided by 8.

As per the question statement, a number "n" gives a remainder of 5 when it is divided by 16.

We are required to calculate the remainder when "n" is divided by 8.

To solve this question, we need to know the relation between Dividend, Quotient, Divisor and Remainder.

[(Quotient * Divisor) + Remainder = Dividend]

Here, (Divisor = 16), (Dividend = "n"), (remainder = 5) and let our Quotient be "x".

Now, we will form a linear equation in one variable, based on the above mentioned relation between Dividend, Quotient, Divisor and Remainder and the conditions mentioned in the question statement, i.e.,

$\frac{n-5}{16}=x\\ or, (16x+5)=n\\or, [2(8x)+5}=n\\or, [8(2x)+5]=n$...(where "x" is any positive integer)

Assuming (2x = y), we get that

$(8y+5)=n\\or, \frac{n-5}{8}=x$

That is, the same number "n" will give a remainder of 5 when divided by 8.

• Remainder: When a number cannot exactly divide another number, the left over amount is know as the remainder of that division.

• Linear Equation: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and thus, comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c)  where, 'm' is the slope and 'b' is the y-intercept.

To learn more about Remainder, click on the link below.

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