Question

If the number is divided by 783 it leaves 48 as a remainder and the same number is divided by 29 what will be the remainder?

Answer 1

The remainder when the number is divided by 29 is 19.

Given:-

Divisor 1 (d1) = 783

Remainder 1 (r1) = 48

Divisor 2 (d2) = 29

To Find:-

The remainder when the number is divided by 29.

Solution:-

We can completely find out the remainder when the number is divided by 29 by using the following procedure.

As

Divisor 1 (d1) = 783

Remainder 1 (r1) = 48

Divisor 2 (d2) = 29

Remainder 2 (r2) =?

Quotient = k

Let the number divided (dividend) be x.

So, according to the formula,

Dividend = (Divisor*Quotient) + Remainder

$x = (783 \times k) + 48$

Now, let's factorize 783 in terms of 29

$x = (29 \times 27 \times k) + 19 + 29$

$x = 29 \times 27k \: + 29 + 19$

on rearranging,

$x = 29(27k + 1) + 19$

Let, (27k+1) = y

So,

$x = 29y + 19$

Therefore, Remainder = 19

Hence, The remainder when the number is divided by 29 is 19.

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