What least number should be subtracted from 86 to 95031 so that the remainder is exactly divisible by 582?

What least number must be subtracted from 13601 to get a number exactly divisible by 87?

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Discussion :: Numbers - General Questions (Q.No.50)
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First, we will divide 13601 by 87.

Remainder = 29So, 29 must be subtracted from 13601 to get a number exactly divisible by 87.i.e., 13601 − 29 = 13572

Now, we have:

∴ 29 must be subtracted from 13601 to make it divisible by 87.

Concept: Concept for Whole Numbers

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Page 2

What least number must be added to 1056 to get a number exactly divisible by 23?

First, we will divide 1056 by 23.

Required number = 23 − 21 = 2So, 2 must be added to 1056 to make it exactly divisible by 23.i.e., 1056 + 2 = 1058

Now, we have:

∴ 1058 is exactly divisible by 23.

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Page 3

We have to find the largest four digit number divisible by 16 .The largest four-digit number = 9999Therefore, dividend =9999

Divisor =16

Here, we get remainder =15Therefore, 15 must be subtracted from 9999 to get the largest four digit number that is divisible by 16.i.e., 9999 − 15 = 9984

Thus, 9984 is the largest four-digit number that is divisible by 16.

Discussion :: Numbers - General Questions (Q.No.50)

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Lakshmi said: (Nov 23, 2011)
In the previous example we subtract the remainder from divisor and the result is taken as the required number. But in this example we take the remainder as a required number. Why?.. Why this difference?..

Chitra said: (May 23, 2012)
This is because in the previous eg. If we substract 29 from the dividend then 13601 will be exactly divisble by 87.

Soumya said: (Apr 28, 2013)
The Actual rule is: When Remainder < Divisor/2 (half of divisor) then answer will be dividend - remainder = answer. and When Remainder > Divisor/2 (half of divisor) then answer will be dividend +(divisor - remainder)= answer.

Ambrish Nitp said: (Aug 24, 2013)
@Soumya. Thr is no such rule. Please don't confuse others, In previous question it was asked how mch no should be ADDED. To get it divisible by 6, 4 WAS remainder. So (6-4) should be added. In this question is asked what no should be subtracted. From 13601 to get it divisible by 87. Required no is the remainder itself.

Poornamsh said: (Sep 18, 2014)

In previous question remainder coming was 16. If we add 2 to it then it becomes 18 which can be divided by 6. or If we subtract 4 from the 16 it becomes 12 then also it becomes divisible by 6. Similarly in this question remainder coming is 29. So, had the number been 29 less than what it is the remainder would be 0 and hence it would be completely divisible by the divisor. Hence we subtract the remainder.

Alternatively if we add 58 to the dividend then remainder will be 87 then it will be divisible by 87.

Ritvik said: (Aug 11, 2015)
The question statement is wrong. Its saying that the what number should be subtracted from 13601, so that the REMAINDER is divisible by 87.

Inna Reddy Chilakala said: (Feb 25, 2016)
So that the remainder is divisible by 87? For this question only from answers 87 is divisible by 29 only.

Raj said: (Jul 10, 2016)
What least number should be subtracted from 86295031 so that the remainder is exactly divisible by 582? Can anyone answer this question?

Vijay Mittal said: (Dec 8, 2016)
In this problem,by subtracting 29 from this number we get 13572. 1 + 3 + 5 + 7+ 2 = 18 And 8 + 7 = 15, 1 + 5 = 6 so 18 is divisible by 6.

Suraj said: (Jul 6, 2017)
If we want to add then divisor-remainder. If we want to subtract then only remainder.

Adi said: (Oct 22, 2017)
The question is wrongly written because they are saying that the REMINDER is divisible by 87. Can anyone tell me that how they are performing the divison0? In question, they have not mentioned a word of dividing the (subtracted from 13601) this calculation by 87.

Supriya said: (Sep 28, 2018)
Exactly right @Adi.

Subro said: (Feb 2, 2019)
Yes, you are right, I agree with you @Adi.

Otem said: (Apr 7, 2021)
Yes, you're right, thanks @Adi.

Mukund said: (Jul 31, 2021)
Right thanks @Adi.

Abinaya Dinesh said: (Oct 28, 2021)
Check the divisors of 87 which is 1, 3, 29 and itself. So when subtracting the given number by the options if it is divisible by 3 then we can choose that as a correct option. 13601 - 29 =13572 to check the divisibility of 3 1+3+5+7+2=18.

Sathya said: (Mon, Jul 11, 2016 11:32:03 AM IST)

Answer:The least number to be subtracted from 86295031 is 145.Solution:Let us divide 86295031 by 582.86295031 (14873 582 _______ 2809 2328 _______ 4815 4656 _______ 1590 1164 _________ 4263 4074 __________ 1891 1746 ___________ 145 ____________

So the required number is 145.

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