Question

Find the least number that must be subtracted from 53678 so that difference is exactly divisible by 384

Answer 1

first of all u divide 53678 by 384
after that subtract the reminder
the ans will be 302..

Answer 2

Answer:

The least number that must be subtracted from 53678 so that difference is exactly divisible by 384 is 302.

Concept:

We know that, the relation of dividend, divisor, quotient and remainder is as follows -

Dividend (Not exactly divisible) = Divisor × Quotient + Remainder ------ (i)

Where Dividend = The number which is being divided

Divisor = The number which divides the dividend

Quotient = The number which is the resultant of the division

Remainder = The number which is left after the division

Now, for any number to be exactly divisible by the divisor, the remainder should be zero. The equation (i) becomes,

Dividend (Exactly divisible) = Divisor × Quotient + 0

Dividend (Exactly divisible) = Divisor × Quotient    -----------------------  (ii)

According to (i), we also have

Dividend (Not exactly divisible) - Remainder = Divisor × Quotient   --- (iii)

Comparing (ii) and (iii), we have

Dividend (Exactly divisible) = Dividend (Not exactly divisible) - Remainder

----------- (iv)

Hence, if the dividend is a number that is not exactly divisible by the divisor, then to make it perfectly divisible, the remainder should be subtracted from the dividend.

Solution:

Let the least number that must be subtracted from 53678 be 'a'.

According to (iv), this least number 'a' is the remainder.

Here, Dividend = 53678

Divisor = 384

Now, 53678 ÷ 384 --->

384 ) 53678 (139

       - 384    

         1527

       - 1152    

           3758

          -3456

              302

∴ Remainder = a = 302

Hence, the least number that must be subtracted from 53678 so that difference is exactly divisible by 384 = a = remainder = 302.

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