Kinda Hard

1. What is difference between the smallest and largest $5$-digit numbers divisible by $11?$

2. What is the least positive integer $n$ such that $1560$ divides $n!?$

3. The six-digit integer $789,XYZ$ consists of six distinct digits and is divisible by $7, 8$ and $9.$ What is the three-digit integer $XYZ?$

4. There is a number formed by $n$ copies of $2020$ and $1$ in the unit place$.$ If this number is divisible by $11,$ what is the smallest possible value of $n?$

5. Modify one digit in the number $31743$ can make it a multiple of $823.$ What is the number after change$?$

(prob be posting these daily)
(not my homework)