Question

Find the largest positive integer that will divide 397, 435 and 541 leaving remainders 6, 10 and 14 respectively.

Answer 1

From question, on dividing 397 by the required number, there is a remainder of 6. This means that 397– 6 = 391 is exactly divisible by the required number i.e., required number is a factor of 391.

Similarly, required positive integer is a factor of 435 – 10 = 425 and 541 – 14 = 527.
∴ Required number = HCF 391, 425 and 527

Now,  391 = 17 × 23
425 = 52 × 17
527 = 17 × 31
∴ Required number = 17.