What are the divisors of 3596?

1, 2, 4, 29, 31, 58, 62, 116, 124, 899, 1798, 3596

There is a total of 12 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 560.

8 even divisors

2, 4, 58, 62, 116, 124, 1798, 3596

4 odd divisors

1, 29, 31, 899

How to compute the divisors of 3596?

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 3596 by each of the numbers from 1 to 3596 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)

3596 / 1 = 3596 (the remainder is 0, so 1 is a divisor of 3596)
3596 / 2 = 1798 (the remainder is 0, so 2 is a divisor of 3596)
3596 / 3 = 1198.6666666667 (the remainder is 2, so 3 is not a divisor of 3596)
...
3596 / 3595 = 1.0002781641168 (the remainder is 1, so 3595 is not a divisor of 3596)
3596 / 3596 = 1 (the remainder is 0, so 3596 is a divisor of 3596)

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 3596 (i.e. 59.96665740226). 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 $\frac{N}{d} = D$ )

3596 / 1 = 3596 (the remainder is 0, so 1 and 3596 are divisors of 3596)
3596 / 2 = 1798 (the remainder is 0, so 2 and 1798 are divisors of 3596)
3596 / 3 = 1198.6666666667 (the remainder is 2, so 3 is not a divisor of 3596)
...
3596 / 58 = 62 (the remainder is 0, so 58 and 62 are divisors of 3596)
3596 / 59 = 60.949152542373 (the remainder is 56, so 59 is not a divisor of 3596)