Final answer:
The greatest number that divides 41, 97, and 181 leaving the same remainder is calculated by finding the GCD of the differences between the numbers, which is 28. So the correct answer is Option C.
Step-by-step explanation:
To find the greatest number that will divide 41, 97, and 181 leaving the same remainder in each case, one needs to calculate the differences between the numbers and then find the greatest common divisor (GCD) of those differences.
The differences between the numbers are as follows:
- 97 - 41 = 56
- 181 - 97 = 84
- 181 - 41 = 140
Next, we find the GCD of 56, 84, and 140, which is 28. Therefore, the greatest number that divides 41, 97, and 181 leaving the same remainder is 28.