37 and 0s

Let

$n=3\underbrace{00\ldots 0}_{99} 7$

To prove that $n$ is divisible by $37$ I'll use two numbers that are clearly divisible by $37$ .

Let's consider

$\begin{aligned} a=37+370+3700+\ldots +37\underbrace{00\ldots 0}_{99}&=4\underbrace{11\ldots 1}_{98} 07\\ &=37\cdot \underbrace{11\ldots 1}_{100} \end{aligned}$

and

$\begin{aligned} b=\underbrace{11\ldots 1}_{99}00 &=111\cdot\underbrace{100100\ldots 100}_{33 \text{ times the string } 100}\\ &=37\cdot\underbrace{300300\ldots 300}_{33 \text{ times the string } 300} \end{aligned}$

We can see that $n=a-b$ so $n$ is divisible by $37$ so the remainder is $R=0$

The quotient is

$\underbrace{11\ldots 1}_{100}-\underbrace{300300\ldots 300}_{33 \text{ times the string } 300}=\underbrace{810810\ldots 810810}_{32 \text{ times the string } 810}811$

Thus the answer is

$\overline{abcdefghi}+R+1=810810810+0+1=\boxed{810810811}$