Find the greatest number which divides 411, 684 and 821 leaving remainders 3, 4 and 5 respectively.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 136
If a number leaves remainder 3 on dividing 411, it divides \(411-3\) exactly. So subtract each remainder; the greatest number that divides all the results is their HCF.
\(411-3=408\), \(684-4=680\), \(821-5=816\)
\(408=2^{3}\times3\times17\)
\(680=2^{3}\times5\times17\)
\(816=2^{4}\times3\times17\)
HCF \(=2^{3}\times17=136\)
136 is larger than every remainder, so the remainders 3, 4 and 5 are possible
The greatest such number is 136.