Question

The largest number which leaves a remainder of 9 and 7 on dividing 285 and 1249 respectively, is:

• A. 6
• B. 12
• C. 138
• D. 46

Answer 1

The correct option is C 138

It is given that the required number when divides 285 and 1249 leaves remainder 9 and 7 respectively.
This means that 285-9=276 and 1249-7=1242 are completely divisible by the required number.
So required number is H.C.F. (276,1242)
By Euclid's division lemma, we have
$1242=276\times 4+138$
$276=138\times 2+0$
$\therefore$ H.C.F. (276,1242)=138