What are the divisors of 3588?

1, 2, 3, 4, 6, 12, 13, 23, 26, 39, 46, 52, 69, 78, 92, 138, 156, 276, 299, 598, 897, 1196, 1794, 3588

There is a total of 24 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 392.

16 even divisors

2, 4, 6, 12, 26, 46, 52, 78, 92, 138, 156, 276, 598, 1196, 1794, 3588

8 odd divisors

1, 3, 13, 23, 39, 69, 299, 897

How to compute the divisors of 3588?

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 3588 by each of the numbers from 1 to 3588 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)

3588 / 1 = 3588 (the remainder is 0, so 1 is a divisor of 3588)
3588 / 2 = 1794 (the remainder is 0, so 2 is a divisor of 3588)
3588 / 3 = 1196 (the remainder is 0, so 3 is a divisor of 3588)
...
3588 / 3587 = 1.0002787844996 (the remainder is 1, so 3587 is not a divisor of 3588)
3588 / 3588 = 1 (the remainder is 0, so 3588 is a divisor of 3588)

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 3588 (i.e. 59.899916527488). 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 $\frac{N}{d} = D$ )

3588 / 1 = 3588 (the remainder is 0, so 1 and 3588 are divisors of 3588)
3588 / 2 = 1794 (the remainder is 0, so 2 and 1794 are divisors of 3588)
3588 / 3 = 1196 (the remainder is 0, so 3 and 1196 are divisors of 3588)
...
3588 / 58 = 61.862068965517 (the remainder is 50, so 58 is not a divisor of 3588)
3588 / 59 = 60.813559322034 (the remainder is 48, so 59 is not a divisor of 3588)