Question

When a natural number 'n' is divided by 4, the remainder is 3. What will be the remainder when (2n + 3) is divided by 4?​

Answer 1

Answer

1

Explanation

Given that a natural number 'n' when divided by 4 gives remainder 3.

So, n can be written in the form of 4q + 3 for some integer q. (Euclid Division Lemma)

n = 4q + 3

→ 2n + 3 = 2(4q + 3) + 3

→ 2n + 3 = 8q + 6 + 3

→ 2n + 3 = 8q + 9

So, (2n + 3) divided by 4 is same as (8q + 9) divided by 4.

Now we will consider (8q + 9)

Since 8q is divisible by 4, the remainder will be given by 9

9 divided by 4 gives remainder 1.

Hence, when (8q + 9) is divided by 4, the remainder is 1

This means that when (2n + 3) is divided by 4, the remainder is 1.

Answer 2

$</p><p>\huge{\tt{\pink{Hello!!! }}}$

When a natural number 'n' is divided by 4, the remainder is 3.

$</p><p>\tt{\red{\therefore {The \: Number \: Is \: Of \: The \: Form \: 4k \:+ \:3 . }}}$

$</p><p>\tt{\orange {=>2n \: + \: 3 }}$

$</p><p>\tt{\blue {=> 2(4k \: + \: 3 ) \: +\: 3 \: = 8k + 9 }}$

When a number of the form 8k + 9, is divided by 4,

$</p><p>\tt{\purple{Result = > \begin{cases}</p><p></p><p>2k \: + \: 2 & \text{Quotient} \\ \\</p><p>1 & \text{Remainder}</p><p></p><p>\end{cases}}}</p><p>$