What are the divisors of 3292?

1, 2, 4, 823, 1646, 3292

There is a total of 6 positive divisors.
The sum of these divisors is 5768.
The arithmetic mean is 961.33333333333.

4 even divisors

2, 4, 1646, 3292

2 odd divisors

1, 823

How to compute the divisors of 3292?

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 3292 by each of the numbers from 1 to 3292 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)

3292 / 1 = 3292 (the remainder is 0, so 1 is a divisor of 3292)
3292 / 2 = 1646 (the remainder is 0, so 2 is a divisor of 3292)
3292 / 3 = 1097.3333333333 (the remainder is 1, so 3 is not a divisor of 3292)
...
3292 / 3291 = 1.0003038590094 (the remainder is 1, so 3291 is not a divisor of 3292)
3292 / 3292 = 1 (the remainder is 0, so 3292 is a divisor of 3292)

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 3292 (i.e. 57.375953151124). 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 $\frac{N}{d} = D$ )

3292 / 1 = 3292 (the remainder is 0, so 1 and 3292 are divisors of 3292)
3292 / 2 = 1646 (the remainder is 0, so 2 and 1646 are divisors of 3292)
3292 / 3 = 1097.3333333333 (the remainder is 1, so 3 is not a divisor of 3292)
...
3292 / 56 = 58.785714285714 (the remainder is 44, so 56 is not a divisor of 3292)
3292 / 57 = 57.754385964912 (the remainder is 43, so 57 is not a divisor of 3292)