2020 · Q16
A number divides 12288, 28200 and 44333 so as to leave the same remainder in each case. What is that number?
Elementary MathematicsHCF and LCM
- A272
- B232
- C221
- D120
Explanation
The required number divides each pairwise difference: 28200 − 12288 = 15912, 44333 − 28200 = 16133, 44333 − 12288 = 32045. Since 16133 − 15912 = 221, and 15912 = 221 × 72, 16133 = 221 × 73, 32045 = 221 × 145, the greatest such number is 221. Any admissible number must divide these differences, and 221 is the greatest integer dividing all three numbers with the same remainder.