Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

We need to find the greatest number which divides 285 and 1249 leaving remainder 9 and 7 respectively.

The required number when divides 285 and 1249 , leaves remainder 9 and 7 , this means $285-9=276$ and $1249-7=1242$ are completely divisible by the number.

Therefore, the required number = H.C.F. of 276 and 1242.

By applying Euclid’s division lemma

$1242=276 \times 4+138$

$276=138 \times 2+0$

Therefore, H.C.F. = 138

Hence, required number is138