Strange and Interesting numbers

I feel like talking again about Maths today. In Mathematics, when you multiply 1, 1, 2... by 8 and then you add the whole number from 1 to 9 to the preceding answer in sequence as shown below, you'll get the number arranged neatly from 1 to 9 for the last digit number for each answer. Interestingly, the digit 9 will never miss its "first seat".

1x8+1=9
12x8+2=98
123x8+3=987
1234x8+4=9876
12345x8+5=98765
123456x8+6=987654
1234567x8+7=9876543
12345678x8+8=98765432
123456789x8+9=987654321

When you calculate the following numbers according to its respective formula, it'll return you the answer of one.

17 x 65,359,477,124,183 = 1,111,111,111,111,111
112 x 9182736455463728191 = 1111111111111111111111
2 + 3 + 6 = 2 + 5 + 4 = 6 + 1 + 4 = 11
3 x 37 = 111
33 x 3367 = 111,111
333 x 333667 = 111,111,111
3333 x 33336667 = 111,111,111,111
33333 x 3333366667 = 111,111,111,111,111

1x9+2=11
12x9+3=111
123x9+4=1111
1234x9+5=11111
12345x9+6=111111
123456x9+7=1111111
1234567x9+8=11111111
12345678x9+9=11111111
123456789x9+10=1111111111

What's the result when you multiply digit 1 to its own number in a sequence as follow? It's just like magic.

1x1=1
11x11=121
111x111=12321
1111x1111=1234321
11111x11111=123454321
111111x111111=12345654321
1111111x1111111=1234567654321
11111111x11111111=123456787654321
111111111x111111111=12345678987654321

To get the answer of 56, simply do the calculations below:

(111+1) / (1+1) = 56
(222+2) / (2+2) = 56
(333+3) / (3+3) = 56
(444+4) / (4+4) = 56
...
(999+9) / (9+9) = 56

Now, look at the following answers. The whole number from 0 to 9 is arranged alternately for each answer. You also observe that its middle digits are the same for all the answers, they are "99999". Don't you think it is strange and weird?

76923x13=0999999
76923x26=1999998
76923x39=2999997
76923x52=3999996
76923x65=4999995
76923x78=5999994
76923x91=6999993
76923x104=7999992
76923x117=8999991
76923x130=9999990

You can get a repetition of two digit numbers in one answer. What? Say again, what're you saying???

122 x 1122334455667789 = 161616161616161616

Below are the easiest ways to get the answer of 8. Give yourself a chance to try.

5 x 7 = 35 and 3+5 = 8
11 x 13 = 143 and 1+4+3 = 8
17 x 19 = 323 and 3+2+3 = 8
29 x 31 = 899 and 8+9+9 = 26 and 2+6 = 8
41 x 43 = 1763 and 1+7+6+3 = 17 and 1+7 = 8
59 x 61 = 3599 and 3+5+9+9 = 26 and 2+6 = 8 ... and etc.

8 is the luckiest number for Chinese as it carries the meaning of "prosper". Well, the presence of eight is always welcomed. Let's welcome the arrival of "Mr. 8..." here.

9x9+7=88
98x9+6=888
987x9+5=8888
9876x9+4=88888
98765x9+3=888888
987654x9+2=8888888

Interesting, right?