What are the divisors of 3091?

1, 11, 281, 3091

There is a total of 4 positive divisors.
The sum of these divisors is 3384.
The arithmetic mean is 846.

4 odd divisors

1, 11, 281, 3091

How to compute the divisors of 3091?

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 3091 by each of the numbers from 1 to 3091 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)

3091 / 1 = 3091 (the remainder is 0, so 1 is a divisor of 3091)
3091 / 2 = 1545.5 (the remainder is 1, so 2 is not a divisor of 3091)
3091 / 3 = 1030.3333333333 (the remainder is 1, so 3 is not a divisor of 3091)
...
3091 / 3090 = 1.0003236245955 (the remainder is 1, so 3090 is not a divisor of 3091)
3091 / 3091 = 1 (the remainder is 0, so 3091 is a divisor of 3091)

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 3091 (i.e. 55.596762495671). 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 $\frac{N}{d} = D$ )

3091 / 1 = 3091 (the remainder is 0, so 1 and 3091 are divisors of 3091)
3091 / 2 = 1545.5 (the remainder is 1, so 2 is not a divisor of 3091)
3091 / 3 = 1030.3333333333 (the remainder is 1, so 3 is not a divisor of 3091)
...
3091 / 54 = 57.240740740741 (the remainder is 13, so 54 is not a divisor of 3091)
3091 / 55 = 56.2 (the remainder is 11, so 55 is not a divisor of 3091)