What are the divisors of 3592?

1, 2, 4, 8, 449, 898, 1796, 3592

There is a total of 8 positive divisors.
The sum of these divisors is 6750.
The arithmetic mean is 843.75.

6 even divisors

2, 4, 8, 898, 1796, 3592

2 odd divisors

1, 449

How to compute the divisors of 3592?

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 3592 by each of the numbers from 1 to 3592 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)

3592 / 1 = 3592 (the remainder is 0, so 1 is a divisor of 3592)
3592 / 2 = 1796 (the remainder is 0, so 2 is a divisor of 3592)
3592 / 3 = 1197.3333333333 (the remainder is 1, so 3 is not a divisor of 3592)
...
3592 / 3591 = 1.0002784739627 (the remainder is 1, so 3591 is not a divisor of 3592)
3592 / 3592 = 1 (the remainder is 0, so 3592 is a divisor of 3592)

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 3592 (i.e. 59.933296255087). 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 $\frac{N}{d} = D$ )

3592 / 1 = 3592 (the remainder is 0, so 1 and 3592 are divisors of 3592)
3592 / 2 = 1796 (the remainder is 0, so 2 and 1796 are divisors of 3592)
3592 / 3 = 1197.3333333333 (the remainder is 1, so 3 is not a divisor of 3592)
...
3592 / 58 = 61.931034482759 (the remainder is 54, so 58 is not a divisor of 3592)
3592 / 59 = 60.881355932203 (the remainder is 52, so 59 is not a divisor of 3592)