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Question
Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.
Solution
The required number when divides 280 and 1245 leaves the remainder 4 and 3, this means 280 4 – 216 and 1245 – 3 = 1245 – 3 = 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 the required numbers is 138.
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