Number 73 in the decimal system is represented as 91 in some other number system; What will be the remainder if a number 364065 of that number system is divided by 7?

First, we need to determine the base of the number system where 73 (in decimal) is represented as 91.

We know that 91 in the other number system is equal to 73 in decimal. This means that 9*x + 1 = 73, where x is the base of the other number system. Solving for x, we get x = 8.

So, the number system is base 8 (or octal).

Next, we need to convert the number 364065 from octal to decimal.

Using the base 8 system, this conversion would look like:

58^0 + 68^1 + 08^2 + 48^3 + 68^4 + 38^5 = 5 + 48 + 0 + 2048 + 24576 + 786432 = 810109

Now, we need to find the remainder when 810109 is divided by 7.

810109 ÷ 7 = 115729 remainder 4

So, the remainder when the number 364065 of the base 8 number system is divided by 7 is 4.