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138.

What is required is the largest number n such that:

285 = jn + 9

1249 = kn + 7

So subtract the required remainders and then find the hcf of the results:

285 - 9 = 276

1249 - 7 = 1242

Find hcf of 276 and 1242:

1242 / 276 = 4 r 138

276 / 138 = 2 r 0

hcf of 276 and 1242 is 138.

Thus 138 is the largest number to divide 285 with a remainder of 9 and divides 1249 with a remainder of 7.

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Q: Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively?
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