Question

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

Answer 1

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 x 4 + 138

276 = 138 x 2 + 0.

Therefore, H.C.F. = 138

Hence, required number is 138