Find the greatest number which divides 412, 709 and 969 leaving remainders 5, 6 and 7 respectively.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 37
Taking away each remainder leaves numbers that the divisor divides exactly, so the greatest such divisor is their HCF.
\(412-5=407\), \(709-6=703\), \(969-7=962\)
\(407=11\times37\), \(703=19\times37\), \(962=2\times13\times37\)
HCF \(=37\)
The greatest such number is 37.
Why the other options are incorrect
Option (1) 74 — Incorrect. 412 divided by 74 leaves remainder 42, not 5.
Option (2) 11 — Incorrect. 709 divided by 11 leaves remainder 5, not 6.
Option (3) 19 — Incorrect. 412 divided by 19 leaves remainder 13, not 5.