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When the numbers 8651, 8018 and 7807 were divided by the greatest number x, then the remainder in each case was the same. The value of x is:
Question

When the numbers 8651, 8018 and 7807 were divided by the greatest number x, then the remainder in each case was the same. The value of x is:

A.

119

B.

132

C.

207

D.

211

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

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