On dividing a number by 413, we get 58 as remainder. On dividing the same number by 59, what will be the remainder? 

Given the problem, let's denote the number as (N). According to the problem, when (N) is divided by 413, the remainder is 58. This can be written as:

[ N = 413k + 58 ]

where (k) is some integer.

We need to find the remainder when (N) is divided by 59. First, we notice that 413 can be expressed in terms of 59, since \((413 = 59 \times 7)\).

So, substitute 413 in the equation:Taking modulo 59 on both sides:\([ N = (59 \times 7)k + 58 ] \)

\([ N \mod 59 = (59 \times 7k + 58) \mod 59 ] \)

Since (59 \times 7k) is divisible by 59, it leaves a remainder of 0:

\([ N \mod 59 = 58 \mod 59 ] \)

Therefore, the remainder when (N) is divided by 59 is:

[ 58 ]

Since 58 is less than 59, the remainder is simply 58.

So, the correct answer is:

3. 58