Question

1,2,3,4,5..............76 digits is divided by 16, what is the remainder

Answer 1

we know that sum of first n natural numbers =n(n+1)÷2 so substitute 76 in place of n you will get 2926 if you divide it with 16 you will get 7 as reminder

Answer 2

Correct Question

1234567.....  (till 76 digits) is divided by 16. What is the remainder?

Answer

The remainder is 0

Given

1234567.....  (till 76 digits) is divided by 16.

To Find

The Remainder

Solution

Here we are given 1234567.....  (till 76 digits)

Therefore, we can infer that

• This is one whole number with 7 digits
• The digits progress successively from 1.

Since we are dividing the number by 16, we need to check the same by the divisibility test.

Any number is divisible by 16 if its last 4 digits are divisible by 16.

Therefore, we need to find the last 4 digits.

We have

12345678910........

1-10 make up 11 digits of the number.

Now we need

76-11

= 65 more digits.

After 10, every number till 99 takes up 2 digits.

So, the next 64 digits will be made up of 32 numbers i.e

from 11 to (10 + 32)

= from 11 to 42

Hence the 76th digit will be 4 of 43

So we get the number like this-

123456789.....41424

We observe that the last 4 digits are 1424.

On dividing 1424 by 16 we get,

$\hspace{0.5cm}89\\16\overline{)1424}\\\hspace{0.5 cm}-128\\= 144\\-144\\=0$

Since itis is completely divisible by 1, the remainder will be 0.

Hence, the remainder is 0

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