Correct option is D
Given:
The numbers are 8651, 8018, and 7807
We need to find the greatest number x that divides these numbers, leaving the same remainder in each case
Concept Used:
The value of x is the Highest Common Factor (HCF) of the differences between these numbers.
According to the property:
K = HCF [a - b, b - c, c - a]
Solution:
x = HCF [8651 - 8018, 8018 - 7807, 8651 - 7807]
Absolute differences between the numbers:
8651 - 8018 = 633
8018 - 7807 = 211
8651 - 7807 = 844
Now, HCF of the differences: 633, 211, and 844.
Since 211 is a prime number, check if it divides the other two differences:
633 ÷ 211 = 3
844 ÷ 211 = 4
As 211 is a common factor of all three differences, the HCF of 633, 211, and 844 is 211
Thus, the value of x is 211