What are the divisors of 3260?

1, 2, 4, 5, 10, 20, 163, 326, 652, 815, 1630, 3260

There is a total of 12 positive divisors.
The sum of these divisors is 6888.
The arithmetic mean is 574.

8 even divisors

2, 4, 10, 20, 326, 652, 1630, 3260

4 odd divisors

1, 5, 163, 815

How to compute the divisors of 3260?

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 3260 by each of the numbers from 1 to 3260 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)

3260 / 1 = 3260 (the remainder is 0, so 1 is a divisor of 3260)
3260 / 2 = 1630 (the remainder is 0, so 2 is a divisor of 3260)
3260 / 3 = 1086.6666666667 (the remainder is 2, so 3 is not a divisor of 3260)
...
3260 / 3259 = 1.0003068425898 (the remainder is 1, so 3259 is not a divisor of 3260)
3260 / 3260 = 1 (the remainder is 0, so 3260 is a divisor of 3260)

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 3260 (i.e. 57.096409694481). 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 $\frac{N}{d} = D$ )

3260 / 1 = 3260 (the remainder is 0, so 1 and 3260 are divisors of 3260)
3260 / 2 = 1630 (the remainder is 0, so 2 and 1630 are divisors of 3260)
3260 / 3 = 1086.6666666667 (the remainder is 2, so 3 is not a divisor of 3260)
...
3260 / 56 = 58.214285714286 (the remainder is 12, so 56 is not a divisor of 3260)
3260 / 57 = 57.19298245614 (the remainder is 11, so 57 is not a divisor of 3260)