Find the largest number which divides 203, 359, 437 and 593 leaving remainder 8 in each case.

Given:

The numbers are 203, 359, 437, and 593, each leaving a remainder of 8.

Formula used:

To find the largest number which divides the given numbers leaving the same remainder, find the HCF (Highest Common Factor) of the differences between the numbers.

Calculations:

Subtract 8 from each number:

203 - 8 = 195

359 - 8 = 351

437 - 8 = 429

593 - 8 = 585

Now, find the HCF of 195, 351, 429, and 585:

First, find the HCF of 195 and 351:

⇒ HCF(195, 351) = 39

Next, find the HCF of 39 and 429:

⇒ HCF(39, 429) = 39

Finally, find the HCF of 39 and 585:

⇒ HCF(39, 585) = 39

∴ The correct answer is option 1.