Question

find the least number that should be added to 36516,so that the result is exactly divisible by 456

Answer 1

Hi ,

By using division algorithm:
************************************
Dividend = divisor × quotient +

remainder

***********************************************

According to the problem ,

Dividend = 36516

Divisor = 456

36516 = 456 × 80 + 36

To find the least number which

should be added to dividend

We use following rule :

least number = divisor - remainder




least number = 456 - 36 = 420




Therefore Required least number =

420

420 is the least number which should

be added to the 36516 so that the

new Dividend is exactly divisible by

456.

Verification:
***************
New dividend = 36516 + 420 = 36936

36936 = 456 × 81 + 0

Remainder = 0

36936 is exactly divisible by 456.

I hope this will useful to you.

******

Answer 2

Answer:

Step-by-step explanation:

Concept:

An algorithm for dividing two integers, N and D, into their quotient and/or remainder, or the product of Euclidean division, is known as a division algorithm. Some are done by hand, while software and digital circuit designs are used for others.

There are two basic types of division algorithms: slow division and quick division. Each cycle of slow division algorithms yields one digit of the final quotient. Restoration, non-performing restoration, non-restoring, and SRT division are a few examples of sluggish division. Fast division techniques yield twice as many digits of the final quotient on each repetition, starting with a close approximation of the ultimate quotient. These include the Newton-Raphson and Goldschmidt algorithms.

Fast multiplication algorithms can be used thanks to these algorithms' variations. As a result, the computer time increases for large integers.

Regardless of the multiplication method employed, the time required for a division is equal to the time required for a multiplication up to a constant factor.

                  $Dividend=divisor\times quotient+remainder$

Given:

Dividend = $36516$

Divisor    = $456$

Find:

We have to find the least number that should be added to $36516$ so that the result is exactly divisible by $456.$

Solution:

Given that Dividend = $36516$

                  Divisor    = $456$

Applying the algorithmic rule for division

$Dividend=divisor\times quotient+remainder$

$36516=456\times80+36$

$least number = divisor - remainder$

                    $= 456 - 36$

                    $=420$

Verification method:

New dividend $= 36516 + 420$

                       $= 36936$

$Dividend=divisor\times quotient+remainder$

$36936 = 456 \times 81 + 0$

Remainder = $0$

$36936$ is exactly divisible by $456.$

Therefore, adding $420$ to $36516$ is the smallest number necessary to make the result exactly divisible by $456$.

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