Multiple choice

When 7865, 8118 and 8624 are divided by the greatest number (x), the remainder in each case is same. The sum of the digits of (x) is:

  1. 9

  2. 11

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When dividing 7865, 8118, and 8624 by the same number with equal remainders, the differences between numbers must be divisible by the divisor. Differences: 8118-7865=253, 8624-8118=506, 8624-7865=759. Find HCF of 253, 506, 759. 506=2×253, so HCF is based on 253 and 759. 759=3×253, so HCF=253. Check: 253=11×23. So x=253 (or could be divisors of 253: 1, 11, 23, 253). Testing: if x=23, then 7865÷23=342 remainder 1, 8118÷23=352 remainder 22 - not equal. If x=11, 7865÷11=715 remainder 0, 8118÷11=738 remainder 0, 8624÷11=784 remainder 0 - equal remainders (0). So greatest x with equal remainders is 253. Sum of digits: 2+5+3=10.

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