What are the divisors of 3957?

1, 3, 1319, 3957

There is a total of 4 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 1320.

4 odd divisors

1, 3, 1319, 3957

How to compute the divisors of 3957?

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 3957 by each of the numbers from 1 to 3957 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)

3957 / 1 = 3957 (the remainder is 0, so 1 is a divisor of 3957)
3957 / 2 = 1978.5 (the remainder is 1, so 2 is not a divisor of 3957)
3957 / 3 = 1319 (the remainder is 0, so 3 is a divisor of 3957)
...
3957 / 3956 = 1.0002527805865 (the remainder is 1, so 3956 is not a divisor of 3957)
3957 / 3957 = 1 (the remainder is 0, so 3957 is a divisor of 3957)

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 3957 (i.e. 62.904689809266). 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 $\frac{N}{d} = D$ )

3957 / 1 = 3957 (the remainder is 0, so 1 and 3957 are divisors of 3957)
3957 / 2 = 1978.5 (the remainder is 1, so 2 is not a divisor of 3957)
3957 / 3 = 1319 (the remainder is 0, so 3 and 1319 are divisors of 3957)
...
3957 / 61 = 64.868852459016 (the remainder is 53, so 61 is not a divisor of 3957)
3957 / 62 = 63.822580645161 (the remainder is 51, so 62 is not a divisor of 3957)