Problem:
The largest number less than 100 divisible by 15 is decreased by 5. Which of these is a factor of the resultant number: A)23 B)25 C)17 D)19?

Solution:
To solve this problem, we need to find the largest number less than 100 that is divisible by 15 and then subtract 5 from it. We can then check which of the given options is a factor of the resultant number.

Finding the largest number divisible by 15:
To find the largest number less than 100 divisible by 15, we need to divide 100 by 15 and take the floor value of the result.

Floor(100 / 15) = 6

So, the largest number less than 100 divisible by 15 is 6 * 15 = 90.

Subtracting 5 from the resultant number:
Now, we need to subtract 5 from 90.

90 - 5 = 85

Checking for factors:
Next, we need to check which of the given options is a factor of 85.

A) 23 is not a factor of 85 because 85 divided by 23 leaves a remainder of 16.
B) 25 is not a factor of 85 because 85 divided by 25 leaves a remainder of 10.
C) 17 is not a factor of 85 because 85 divided by 17 leaves a remainder of 0.
D) 19 is not a factor of 85 because 85 divided by 19 leaves a remainder of 8.

Therefore, the only option that is a factor of the resultant number 85 is C) 17.

Conclusion:
The factor of the resultant number obtained by subtracting 5 from the largest number less than 100 divisible by 15 is C) 17.

17