Question

A hundred and twenty digit number is formed by writing the first x natural numbers in front of each other as
12345678910111213...... Find the remainder when this number is divided by 8.

Answer 1

have you tried anything ?

Answer 2

firstly,i cant interpete it clearly

Answer 3

you have a number formed by putting first few natural numbers in a row :

1
2
3
4
5
6
7
8
9
10
11
12
...

Answer 4

you need to find the remainder when it gets divided by 8

Answer 5

which number is the required dividend?

Answer 6

you should spend sometime and try out the problem on your own to get a feel of it

Answer 7

what do you mean by `2 digit number`
i don't see that in question ?

Answer 8

100 digit ?

Answer 9

read the question fully first,
please don't post questions here w/o trying them on your own >.<

Answer 10

I'd say the first step is to figure out what the last number in the string would be.

The first 9 digits are the numbers 1-9. The next 100 digits would be made up of the next 50 numbers (10-59), leaving us with 11 more digits to worry about. These last few digits would be made up of the numbers 60-64 (10 digits), leaving us with one more digit, which would presumably be the 6 from the number 65.

So the number would be
\[12345\dots(63)(64)(6)\]
Just to check that the number of digits is right: http://www.wolframalpha.com/input/?i=123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646

Answer 11

Dividing by 8 is the same as dividing by 2 three times.

The first division would make the last few digits \(\dots1823\).

The second would make them \(\dots5911.5\).

The third would make them \(\dots2955.75\).

Since \(0.75=\dfrac{3}{4}=\dfrac{6}{8}\), what do you think the remainder would be?

Answer 12

Anyway, I don't know if there's a less tedious method, but this is certainly one way to approach the question.