Answer:
Let the unknown number be x. We are given that 25 multiplied by x in base six equals 13305 base six. We can set up the following equation to solve for x:
25x = 13305
To solve for x, we need to first convert 13305 from base six to base ten. This can be done by multiplying each digit by the corresponding power of six and adding the results:
1 x 6^4 + 3 x 6^3 + 3 x 6^2 + 0 x 6^1 + 5 x 6^0 = 1296 + 648 + 108 + 5 = 2057
Therefore, 13305 base six is equal to 2057 in base ten.
Substituting this value into the equation, we get:
25x = 2057
Solving for x, we get:
x = 2057 / 25
x = 82.28
Since we are working in base six, we need to express x in base six. To do this, we can use long division to convert 82.28 from base ten to base six:
6| 82.28
|-------
1 | 2.28
|-------
3.68
1.13
Therefore, 82.28 in base ten is equivalent to 1131.1 in base six.
Therefore, the other number is 1131.1 base six.