When the numbers 7807, 8022 and 8667 were divided by the greatest number x, then the remainder in each case was the same. The sum of the digits of x is:

Correct option is A

Given:

The numbers are 8667, 8022, and 7807

We need to find the greatest number x that divides these numbers, leaving the same remainder in each case, and then calculate the sum of the digits of x

Concept Used:

The value of xx is the Highest Common Factor (HCF) of the absolute differences between these numbers.

According to the property:

K = HCF [|a - b|, |b - c|, |c - a|]

Solution:

x = HCF[|8667 - 8022|, |8022 - 7807|, |8667 - 7807|]

Absolute differences between the numbers:

|8667 - 8022| = 645

|8022 - 7807| = 215

|8667 - 7807| = 860

Now, the HCF of the differences: 645, 215, and 860

HCF = 215

The greatest number x is 215

Sum of digits of 215 = 2 + 1 + 5 = 8