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