What are the divisors of 3269?

1, 7, 467, 3269

There is a total of 4 positive divisors.
The sum of these divisors is 3744.
The arithmetic mean is 936.

4 odd divisors

1, 7, 467, 3269

How to compute the divisors of 3269?

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 3269 by each of the numbers from 1 to 3269 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)

3269 / 1 = 3269 (the remainder is 0, so 1 is a divisor of 3269)
3269 / 2 = 1634.5 (the remainder is 1, so 2 is not a divisor of 3269)
3269 / 3 = 1089.6666666667 (the remainder is 2, so 3 is not a divisor of 3269)
...
3269 / 3268 = 1.000305997552 (the remainder is 1, so 3268 is not a divisor of 3269)
3269 / 3269 = 1 (the remainder is 0, so 3269 is a divisor of 3269)

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 3269 (i.e. 57.175169435691). 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 $\frac{N}{d} = D$ )

3269 / 1 = 3269 (the remainder is 0, so 1 and 3269 are divisors of 3269)
3269 / 2 = 1634.5 (the remainder is 1, so 2 is not a divisor of 3269)
3269 / 3 = 1089.6666666667 (the remainder is 2, so 3 is not a divisor of 3269)
...
3269 / 56 = 58.375 (the remainder is 21, so 56 is not a divisor of 3269)
3269 / 57 = 57.350877192982 (the remainder is 20, so 57 is not a divisor of 3269)