Find the largest number with which when 394 and 658 are divided, they leave remainders of 1 and 3, respectively.

when 394 and 658 are divided by the largest number, they leave remainders of 1 and 3, respectively.

Here we need to subtract the remainders with these respective numbers. Because once the remainder will be subtracted, these numbers will be completely divisible.

So 394-1 = 393

658-3 = 655

The factors of the obtained numbers are given below.

393 ==> $$131\times3$$ 

655 ==> $$131\times5$$

Here 131 is the common factor.

So the largest number is 131 with which when 394 and 658 are divided, they leave remainders of 1 and 3, respectively.