Question

When N is divided by 4, the remainder is 3. What is
the remainder when 2N is divided by 4.


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Answer 1

Answer:

Hope this will help you.......

Answer 2

Step-by-step explanation:

Given:-

N is divided by 4, the remainder is 3

To find:-

What is the remainder when 2N is divided by 4?

Solution:-

Given number = N

Given divisor = 4

If N is divided by 4 then the remainder = 3

N = 4K + 3 --------(1)

Where K is a positive integer

On multiplying 2 both sides then

=> 2×N = 2×(4K+3)

=> 2N = 8K+6

=> 2N = 8K+4+2

=> 2N = (8K+4)+2

=> 2N = 4(2K+1) +2

=> 2N = 4M +2, Where M = 2K+1

The remainder = 2

If 2N is divided by 4 then the remainder = 2

Answer:-

The required remainder for the given problem is 2

Check:-

Consider a number 7

If 7 is divided by 4 then the remainder = 3

then 2×7 = 14 divided by 4 then the remainder = 2

Consider 11

If 11 is divided by 4 then the remainder is 3

then 2×11 = 22 is divided by 4 then the remainder is 2

Used Concept:-

Euclid's Division Lemma:-

For any two positive integers there exists positive integers q and r satisfying a=bq+r,0≤r<b.

Division Rule:-

Dividend= Divisor×Quotient +Remainder.