What are the divisors of 3089?

1, 3089

There is a total of 2 positive divisors.
The sum of these divisors is 3090.
The arithmetic mean is 1545.

2 odd divisors

1, 3089

How to compute the divisors of 3089?

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 3089 by each of the numbers from 1 to 3089 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)

3089 / 1 = 3089 (the remainder is 0, so 1 is a divisor of 3089)
3089 / 2 = 1544.5 (the remainder is 1, so 2 is not a divisor of 3089)
3089 / 3 = 1029.6666666667 (the remainder is 2, so 3 is not a divisor of 3089)
...
3089 / 3088 = 1.0003238341969 (the remainder is 1, so 3088 is not a divisor of 3089)
3089 / 3089 = 1 (the remainder is 0, so 3089 is a divisor of 3089)

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 3089 (i.e. 55.578772926361). 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 $\frac{N}{d} = D$ )

3089 / 1 = 3089 (the remainder is 0, so 1 and 3089 are divisors of 3089)
3089 / 2 = 1544.5 (the remainder is 1, so 2 is not a divisor of 3089)
3089 / 3 = 1029.6666666667 (the remainder is 2, so 3 is not a divisor of 3089)
...
3089 / 54 = 57.203703703704 (the remainder is 11, so 54 is not a divisor of 3089)
3089 / 55 = 56.163636363636 (the remainder is 9, so 55 is not a divisor of 3089)