Find the largest number which divides 410, 751 and 1030, leaving remainder 7 in each case.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 31
A number that leaves remainder 7 divides each given number minus 7 exactly, so the largest such number is the HCF of the three differences.
\(410-7=403\), \(751-7=744\), \(1030-7=1023\)
\(403=13\times31\)
\(744=24\times31\)
\(1023=33\times31\)
13, 24 and 33 have no common factor, so HCF \(=31\)
31 is larger than 7, so a remainder of 7 is possible
The largest such number is 31.