Whats the reminder when 42,527,152,653,425,416,242,624,272,427,215,287

Question

Whats the reminder when 42,527,152,653,425,416,242,624,272,427,215,287 is divided by 16

A. 1
B. 7.
C. 2.
D. 3
E. 9

KarishmaB · Accepted Answer

A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16.
Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it.

42,527,152,653,425,416,242,624,272,427,215,287 = 42,527,152,653,425,416,242,624,272,427,210000 + 5287

The first number is divisible by 16. You just have to find the remainder when you divide 5287 by 16. That will be the remainder when you divide the original number by 16.

5287/16 gives remainder 7.

Answer (B)

sudhir18n · Answer

divisibility by 16 .. take last 4 digits 
5287 mod 16 = 7
hence B

subhashghosh · Answer

I tried the following approach:

42527152653425416242624272427215287/16 = 42527152653425416242624272427215280/16 + 7/16

Now the last two digits of first term, 80 is divisible by 4 and so is the denominator 16.

Again, 80/16 = 20/4 also divides , so remainder = 7

Answer - B

But I'm not 100% convinced with my approach.

sudhir18n · Answer

Hi Subhash, even i doubt your approach.. I tried randomly sum numbers using ur approach, but it doesnt work.. https://staff.argyll.epsb.ca/jreed/math7 ... 1/1104.htm

subhashghosh · Answer

Yup.. I'll wait for experts to opine on this.

dimri10 · Answer

it seems like a wise mehod.kudos

Spidy001 · Answer

@sudhir18n

even though your approach worked here , i dont think it can be generalized that way. It may not yield the right answer all the time.

eg : 2782 when divided by 16 leaves a remainder of 6

but 12782 when divided by 16 leaves a remainder of 14
 
 so if we you get 12782 and were asked to find remainder when divided by 16 
 if you go by 4 digit approach then that would be wrong..

sudhir18n · Answer

are you sure 2782 mod 16 = 6
im getting 14 ..

Spidy001 · Answer

Yeah u r right. I mis calculated that one .

Posted from my mobile device

toughmat · Answer

Can someone pls explain what the approach should be for such a question

Anonymous · Answer

We all know 100 is divisible by 4 so 100x100 is divisible by 4x4. To find the remainder of A divided by 16, we just need the last 4 digits.

Amit0507 · Answer

16 is a multiple of 8 and 2. A number can be checked for 8, by dividing the last 3 digits and for 2 by dividing the last digit. Here 287 will result in 7 as a remainder when divided by 8 and 1 when divided by 2. Therefore the remainder is 7*1 = 7. 
Break down the divisor into smaller factors and perform the division check.

suresh8055 · Answer

can we follow this approach every time ? for last 2,3,4 digits and check the divisibility test ?

coolkl · Answer

I used the same approach of 287 div by 8 gives remainder as 7. Now I divided 7 by 2 to get remainder as 1. So my Answer was A, which i now know is wrong. But I dont understand your last step of multiplying 7*1 = 7 as remainder. What's your thought process doing that step ? Any help appreciated.

wishmasterdj · Answer

Used exactly this approach.

took out remainders with both 2 and 8 and then multiplied by them 
and lastly ensure the product < 16

bumpbot · Answer

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Whats the reminder when 42,527,152,653,425,416,242,624,272,427,215,287

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Whats the reminder when 42,527,152,653,425,416,242,624,272,427,215,287

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