Can't factor this

$738=a+\left( 10a+a \right) +\left( 100a+10a+a \right) =123a=123\frac { 9b }{ 6 } \Rightarrow 738=\frac { 369 }{ 2 } b\Rightarrow b=4$

A number which is finished by $8$ needs a number $a$ where $3a$ is also finished by $8$ , because $a + a + a = 8$ . A number that fits in these circumstances is the $6$ .

So: $6 + 66 + 666 = 738$

To find b, just calculate the expression $6 \times 6 = 9b$ Then, the answer is $b = \boxed {4}$

Python 2.7:

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def goal(a):
    return a + int(str(a)*2)\
       + int(str(a)*3) == 738
a = 0
while not goal(a):
    a += 1
b = (6*a)/9.0
print "Answer:", b

$\bar { aaa } =100a+10a+a\\ \bar { aa } =10a+a\\ \bar { a } =a$

We have :

$\bar { aaa } +\bar { aa } +\bar { a } =738$

Rewriting

$100a+10a+a\quad +10a+a+=738\\ \\ \therefore 123\quad a\quad =738\\ a\quad =\quad \frac { 738 }{ 123 } =6$

Finally: $6a\quad =\quad 9b\\ \\ a\quad =\frac { 9 }{ 6 } b\\ \\ 6=\quad 9/6b\\ \\ b=\quad \frac { 6\times 6 }{ 9 } =4\\$

It can be seen that 738 = a+11a+111a = 123a. So a= $\frac{738}{123}$ = 6. Now we have 9b = 6(6) = 36 so b= $\frac{36}{9}$ = 4 yay.

Obviously a < 7 otherwise the concatenation of aaa would be 777>738.

Plus we know that a+a+a = 8 (the last number of 738). Adding this info to the precedent gives us one solution: a = 6. Then b = 4.

Trivial to see that: 0 <= aa + a < 109 < 138

Therefore, 738 >= aaa > 600, hence a = 6 and b = 4.

No need for any equations :)

You really don't need to do the sum to get the answer. which number multiplied by 3 ends with 8 , its 6 you can check. 6+66+666=738. Now 6 6=9 b, so b= 4. Now you may call me crooked but well you have the answer.