What are the divisors of 3059?

1, 7, 19, 23, 133, 161, 437, 3059

There is a total of 8 positive divisors.
The sum of these divisors is 3840.
The arithmetic mean is 480.

8 odd divisors

1, 7, 19, 23, 133, 161, 437, 3059

How to compute the divisors of 3059?

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 3059 by each of the numbers from 1 to 3059 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)

3059 / 1 = 3059 (the remainder is 0, so 1 is a divisor of 3059)
3059 / 2 = 1529.5 (the remainder is 1, so 2 is not a divisor of 3059)
3059 / 3 = 1019.6666666667 (the remainder is 2, so 3 is not a divisor of 3059)
...
3059 / 3058 = 1.0003270111184 (the remainder is 1, so 3058 is not a divisor of 3059)
3059 / 3059 = 1 (the remainder is 0, so 3059 is a divisor of 3059)

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 3059 (i.e. 55.308227236099). 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 $\frac{N}{d} = D$ )

3059 / 1 = 3059 (the remainder is 0, so 1 and 3059 are divisors of 3059)
3059 / 2 = 1529.5 (the remainder is 1, so 2 is not a divisor of 3059)
3059 / 3 = 1019.6666666667 (the remainder is 2, so 3 is not a divisor of 3059)
...
3059 / 54 = 56.648148148148 (the remainder is 35, so 54 is not a divisor of 3059)
3059 / 55 = 55.618181818182 (the remainder is 34, so 55 is not a divisor of 3059)