What are the divisors of 3580?

1, 2, 4, 5, 10, 20, 179, 358, 716, 895, 1790, 3580

There is a total of 12 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 630.

8 even divisors

2, 4, 10, 20, 358, 716, 1790, 3580

4 odd divisors

1, 5, 179, 895

How to compute the divisors of 3580?

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 3580 by each of the numbers from 1 to 3580 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)

3580 / 1 = 3580 (the remainder is 0, so 1 is a divisor of 3580)
3580 / 2 = 1790 (the remainder is 0, so 2 is a divisor of 3580)
3580 / 3 = 1193.3333333333 (the remainder is 1, so 3 is not a divisor of 3580)
...
3580 / 3579 = 1.0002794076558 (the remainder is 1, so 3579 is not a divisor of 3580)
3580 / 3580 = 1 (the remainder is 0, so 3580 is a divisor of 3580)

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 3580 (i.e. 59.833101206606). 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 $\frac{N}{d} = D$ )

3580 / 1 = 3580 (the remainder is 0, so 1 and 3580 are divisors of 3580)
3580 / 2 = 1790 (the remainder is 0, so 2 and 1790 are divisors of 3580)
3580 / 3 = 1193.3333333333 (the remainder is 1, so 3 is not a divisor of 3580)
...
3580 / 58 = 61.724137931034 (the remainder is 42, so 58 is not a divisor of 3580)
3580 / 59 = 60.677966101695 (the remainder is 40, so 59 is not a divisor of 3580)