What are the divisors of 3231?

1, 3, 9, 359, 1077, 3231

There is a total of 6 positive divisors.
The sum of these divisors is 4680.
The arithmetic mean is 780.

6 odd divisors

1, 3, 9, 359, 1077, 3231

How to compute the divisors of 3231?

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 3231 by each of the numbers from 1 to 3231 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)

3231 / 1 = 3231 (the remainder is 0, so 1 is a divisor of 3231)
3231 / 2 = 1615.5 (the remainder is 1, so 2 is not a divisor of 3231)
3231 / 3 = 1077 (the remainder is 0, so 3 is a divisor of 3231)
...
3231 / 3230 = 1.0003095975232 (the remainder is 1, so 3230 is not a divisor of 3231)
3231 / 3231 = 1 (the remainder is 0, so 3231 is a divisor of 3231)

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 3231 (i.e. 56.841885964489). 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 $\frac{N}{d} = D$ )

3231 / 1 = 3231 (the remainder is 0, so 1 and 3231 are divisors of 3231)
3231 / 2 = 1615.5 (the remainder is 1, so 2 is not a divisor of 3231)
3231 / 3 = 1077 (the remainder is 0, so 3 and 1077 are divisors of 3231)
...
3231 / 55 = 58.745454545455 (the remainder is 41, so 55 is not a divisor of 3231)
3231 / 56 = 57.696428571429 (the remainder is 39, so 56 is not a divisor of 3231)