Try splitting the number

1,000,063 = $10^6$ + 63,

So if 1,000,063 number divided by other number(n) to get remainder =63,

The number should be multiple of $10^6$ and must be greater than 63,

So as $10^6$ = $2^6$ . $5^6$ ,

So number of divisors for $10^6$ = 7(7) = 49.

now we have to exclude $1,2,4,5,8,16,32,10,20,25,40,50$ (since they are greater than 63),

So we get total number of values of n = 49 - 12 = 37.

$\begin{aligned} 1000063 & \equiv 63 \pmod {n} \\ \implies 1000000 & \equiv 0 \pmod {n} \end{aligned}$

This means $1000000$ is divisible by $n$ or $n$ is a factor of $1000000$ . Since $1000000 = 2^6 5^6$ , there are $(6+1)(6+1) = 49$ factors.

Out of these 49 factors, $1000063 \mod = \begin{cases} 63-n & \text{if }n < 63 \\ 63 & \text{if }n > 63 \end{cases}$ .

Since factors smaller than 63 are 1, 2, 4, 8, 16, 32, and 5, 10, 20, 25, 40, 50, a total of 12. Therefore, the number of $n$ that gives a remainder of 63 is $49-12=\boxed{37}$ .