What are the divisors of 6058?

1, 2, 13, 26, 233, 466, 3029, 6058

There is a total of 8 positive divisors.
The sum of these divisors is 9828.
The arithmetic mean is 1228.5.

4 even divisors

2, 26, 466, 6058

4 odd divisors

1, 13, 233, 3029

How to compute the divisors of 6058?

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 6058 by each of the numbers from 1 to 6058 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)

6058 / 1 = 6058 (the remainder is 0, so 1 is a divisor of 6058)
6058 / 2 = 3029 (the remainder is 0, so 2 is a divisor of 6058)
6058 / 3 = 2019.3333333333 (the remainder is 1, so 3 is not a divisor of 6058)
...
6058 / 6057 = 1.0001650982334 (the remainder is 1, so 6057 is not a divisor of 6058)
6058 / 6058 = 1 (the remainder is 0, so 6058 is a divisor of 6058)

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 6058 (i.e. 77.83315488916). 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 $\frac{N}{d} = D$ )

6058 / 1 = 6058 (the remainder is 0, so 1 and 6058 are divisors of 6058)
6058 / 2 = 3029 (the remainder is 0, so 2 and 3029 are divisors of 6058)
6058 / 3 = 2019.3333333333 (the remainder is 1, so 3 is not a divisor of 6058)
...
6058 / 76 = 79.710526315789 (the remainder is 54, so 76 is not a divisor of 6058)
6058 / 77 = 78.675324675325 (the remainder is 52, so 77 is not a divisor of 6058)