What are the divisors of 3291?

1, 3, 1097, 3291

There is a total of 4 positive divisors.
The sum of these divisors is 4392.
The arithmetic mean is 1098.

4 odd divisors

1, 3, 1097, 3291

How to compute the divisors of 3291?

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 3291 by each of the numbers from 1 to 3291 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)

3291 / 1 = 3291 (the remainder is 0, so 1 is a divisor of 3291)
3291 / 2 = 1645.5 (the remainder is 1, so 2 is not a divisor of 3291)
3291 / 3 = 1097 (the remainder is 0, so 3 is a divisor of 3291)
...
3291 / 3290 = 1.0003039513678 (the remainder is 1, so 3290 is not a divisor of 3291)
3291 / 3291 = 1 (the remainder is 0, so 3291 is a divisor of 3291)

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 3291 (i.e. 57.367238037054). 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 $\frac{N}{d} = D$ )

3291 / 1 = 3291 (the remainder is 0, so 1 and 3291 are divisors of 3291)
3291 / 2 = 1645.5 (the remainder is 1, so 2 is not a divisor of 3291)
3291 / 3 = 1097 (the remainder is 0, so 3 and 1097 are divisors of 3291)
...
3291 / 56 = 58.767857142857 (the remainder is 43, so 56 is not a divisor of 3291)
3291 / 57 = 57.736842105263 (the remainder is 42, so 57 is not a divisor of 3291)