What are the divisors of 3266?

1, 2, 23, 46, 71, 142, 1633, 3266

There is a total of 8 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 648.

4 even divisors

2, 46, 142, 3266

4 odd divisors

1, 23, 71, 1633

How to compute the divisors of 3266?

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 3266 by each of the numbers from 1 to 3266 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)

3266 / 1 = 3266 (the remainder is 0, so 1 is a divisor of 3266)
3266 / 2 = 1633 (the remainder is 0, so 2 is a divisor of 3266)
3266 / 3 = 1088.6666666667 (the remainder is 2, so 3 is not a divisor of 3266)
...
3266 / 3265 = 1.0003062787136 (the remainder is 1, so 3265 is not a divisor of 3266)
3266 / 3266 = 1 (the remainder is 0, so 3266 is a divisor of 3266)

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 3266 (i.e. 57.148928248918). 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 $\frac{N}{d} = D$ )

3266 / 1 = 3266 (the remainder is 0, so 1 and 3266 are divisors of 3266)
3266 / 2 = 1633 (the remainder is 0, so 2 and 1633 are divisors of 3266)
3266 / 3 = 1088.6666666667 (the remainder is 2, so 3 is not a divisor of 3266)
...
3266 / 56 = 58.321428571429 (the remainder is 18, so 56 is not a divisor of 3266)
3266 / 57 = 57.298245614035 (the remainder is 17, so 57 is not a divisor of 3266)