What are the divisors of 3908?

1, 2, 4, 977, 1954, 3908

There is a total of 6 positive divisors.
The sum of these divisors is 6846.
The arithmetic mean is 1141.

4 even divisors

2, 4, 1954, 3908

2 odd divisors

1, 977

How to compute the divisors of 3908?

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 3908 by each of the numbers from 1 to 3908 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)

3908 / 1 = 3908 (the remainder is 0, so 1 is a divisor of 3908)
3908 / 2 = 1954 (the remainder is 0, so 2 is a divisor of 3908)
3908 / 3 = 1302.6666666667 (the remainder is 2, so 3 is not a divisor of 3908)
...
3908 / 3907 = 1.0002559508574 (the remainder is 1, so 3907 is not a divisor of 3908)
3908 / 3908 = 1 (the remainder is 0, so 3908 is a divisor of 3908)

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 3908 (i.e. 62.513998432351). 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 $\frac{N}{d} = D$ )

3908 / 1 = 3908 (the remainder is 0, so 1 and 3908 are divisors of 3908)
3908 / 2 = 1954 (the remainder is 0, so 2 and 1954 are divisors of 3908)
3908 / 3 = 1302.6666666667 (the remainder is 2, so 3 is not a divisor of 3908)
...
3908 / 61 = 64.065573770492 (the remainder is 4, so 61 is not a divisor of 3908)
3908 / 62 = 63.032258064516 (the remainder is 2, so 62 is not a divisor of 3908)