Final answer:
To find the greatest number that divides 21, 69, and 93 with the same remainder, we calculate the GCD of the differences between the numbers. The greatest number is 24.
Step-by-step explanation:
The question asks us to find the greatest number that will divide 21, 69, and 93 and leave the same remainder in each case. To do this, we need to find the greatest common divisor (GCD) of the differences between the numbers.
By subtracting the smallest number from the other two, we get the pairs (69-21) and (93-21), which result in 48 and 72, respectively. The GCD of 48 and 72 is 24, which means the answer is c. 24.
This number will divide both 48 and 72 perfectly, which means it is the greatest number that can divide 21, 69, and 93 while leaving the same remainder.