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Question
Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.
Solution
The require 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
∴ The required number = HCF of 276 and 1242
By applying Euclid’s division lemma
1242 = 276 × 4 + 138
276 = 138 × 2 + 0
∴ HCF = 138
Hence remainder is = 0
Hence required number is 138
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