arrow
arrow
arrow
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 i
Question

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:

A.

8

B.

9

C.

6

D.

7

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

Free Tests

Free
Must Attempt

SSC MTS GA Section Test 01 (With New Interface)

languageIcon English
  • pdpQsnIcon25 Questions
  • pdpsheetsIcon75 Marks
  • timerIcon20 Mins
languageIcon English
Free
Must Attempt

SSC MTS PYP (30 Sep 2024 S1) (With New Interface)

languageIcon English
  • pdpQsnIcon90 Questions
  • pdpsheetsIcon270 Marks
  • timerIcon90 Mins
languageIcon English
Free
Must Attempt

SSC CHSL Tier-I 2025 Mock 01 (With New Interface)

languageIcon English
  • pdpQsnIcon100 Questions
  • pdpsheetsIcon200 Marks
  • timerIcon60 Mins
languageIcon English
test-prime-package

Access ‘SSC GD’ Mock Tests with

  • 60000+ Mocks and Previous Year Papers
  • Unlimited Re-Attempts
  • Personalised Report Card
  • 500% Refund on Final Selection
  • Largest Community
students-icon
250k+ students have already unlocked exclusive benefits with Test Prime!
Our Plans
Monthsup-arrow