What are the divisors of 3913?

1, 7, 13, 43, 91, 301, 559, 3913

There is a total of 8 positive divisors.
The sum of these divisors is 4928.
The arithmetic mean is 616.

8 odd divisors

1, 7, 13, 43, 91, 301, 559, 3913

How to compute the divisors of 3913?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 3913 by each of the numbers from 1 to 3913 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

3913 / 1 = 3913 (the remainder is 0, so 1 is a divisor of 3913)
3913 / 2 = 1956.5 (the remainder is 1, so 2 is not a divisor of 3913)
3913 / 3 = 1304.3333333333 (the remainder is 1, so 3 is not a divisor of 3913)
...
3913 / 3912 = 1.0002556237219 (the remainder is 1, so 3912 is not a divisor of 3913)
3913 / 3913 = 1 (the remainder is 0, so 3913 is a divisor of 3913)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 3913 (i.e. 62.553976692134). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

3913 / 1 = 3913 (the remainder is 0, so 1 and 3913 are divisors of 3913)
3913 / 2 = 1956.5 (the remainder is 1, so 2 is not a divisor of 3913)
3913 / 3 = 1304.3333333333 (the remainder is 1, so 3 is not a divisor of 3913)
...
3913 / 61 = 64.147540983607 (the remainder is 9, so 61 is not a divisor of 3913)
3913 / 62 = 63.112903225806 (the remainder is 7, so 62 is not a divisor of 3913)