One number written by 2014 number 8 in a row. Q. How many units should be added to the number to divide by 36?

I'm really happy if you can help me!

Mar 31, 2018

$2$

Explanation:

First, $36 = 9 \cdot 4$. If our number with 2014 8's is $n$

$\frac{n}{36} = \frac{n}{4} \cdot \frac{1}{9}$

If we divide $n$ by $4$, we would have 2014 2's.

$888. \ldots 8 : 4 = 222. . .2 = a$

Now we need to divide $a$ by $9$. A number can be divide by $9$, if the cross sum can be divide by $9$.
$q \left(a\right) = \left(2 + 2 + 2. . . + 2\right) = 2014 \cdot 2 = 4028$
$q \left(4028\right) = 14$

The next factor of $9$ would be $18$.
$18 - 14 = 4$

Therefore, we need to raise the cross sum by $4$. Since we are adding 8's which are getting divide by $4$, we are actually adding 2's. The answer is...
$\frac{4}{2} = 2$
...8's have to be added.