Multiple choice

When 1878, 4069 and 5008 are divided by the greatest number (x), then the remainder in each case is the same. The sum of the digits of (x) is?

  1. 9

  2. 7

  3. 8

  4. 6

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If the same remainder r is obtained when dividing 1878, 4069, and 5008 by x, then x divides all pairwise differences: 4069-1878=2191, 5008-4069=939, and 5008-1878=3130. The HCF of these differences is x. Computing gcd(2191, 939, 3130) = 313. Sum of digits: 3+1+3=7.