Question

Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.

Answer 1

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.