What are the divisors of 3232?

1, 2, 4, 8, 16, 32, 101, 202, 404, 808, 1616, 3232

There is a total of 12 positive divisors.
The sum of these divisors is 6426.
The arithmetic mean is 535.5.

10 even divisors

2, 4, 8, 16, 32, 202, 404, 808, 1616, 3232

2 odd divisors

1, 101

How to compute the divisors of 3232?

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 3232 by each of the numbers from 1 to 3232 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)

3232 / 1 = 3232 (the remainder is 0, so 1 is a divisor of 3232)
3232 / 2 = 1616 (the remainder is 0, so 2 is a divisor of 3232)
3232 / 3 = 1077.3333333333 (the remainder is 1, so 3 is not a divisor of 3232)
...
3232 / 3231 = 1.0003095017023 (the remainder is 1, so 3231 is not a divisor of 3232)
3232 / 3232 = 1 (the remainder is 0, so 3232 is a divisor of 3232)

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 3232 (i.e. 56.850681614208). 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 $\frac{N}{d} = D$ )

3232 / 1 = 3232 (the remainder is 0, so 1 and 3232 are divisors of 3232)
3232 / 2 = 1616 (the remainder is 0, so 2 and 1616 are divisors of 3232)
3232 / 3 = 1077.3333333333 (the remainder is 1, so 3 is not a divisor of 3232)
...
3232 / 55 = 58.763636363636 (the remainder is 42, so 55 is not a divisor of 3232)
3232 / 56 = 57.714285714286 (the remainder is 40, so 56 is not a divisor of 3232)