correct answer is: a) 24

Explanation

Here,
To find the greatest number, we can use greatest common divisor or (GCD) method.
First, we find the differences between the numbers :
\rightarrow Difference between 147 and 123 = (147 – 123) = 24.
\rightarrow Difference between 195 and 147 = (195 – 147) = 48.
\rightarrow Difference between 195 and 123 = (195 – 123) = 72.
Now, we find the greatest common divisor (GCD) of these differences.
\therefore Greatest common divisor of 24,48 and 72 is =24.
So that, the greatest number that will divide 123,147 and 195 to leave the same remainder in each case is 24.
Ans: The greatest number is 24.

An alternative way to phrase this particular math query is possible:

1. Determine the largest number that, when divided into 123, 147 and 195, leaves the same remainder in each case.
2. Find the greatest divisor that, when used to divide 123, 147 and 195, results in the same remainder for each division.
3. What is the greatest number that can divide 123, 147 and 195, leaving the same remainder in each division?