What are the divisors of 4058?

1, 2, 2029, 4058

There is a total of 4 positive divisors.
The sum of these divisors is 6090.
The arithmetic mean is 1522.5.

2 even divisors

2, 4058

2 odd divisors

1, 2029

How to compute the divisors of 4058?

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 4058 by each of the numbers from 1 to 4058 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)

4058 / 1 = 4058 (the remainder is 0, so 1 is a divisor of 4058)
4058 / 2 = 2029 (the remainder is 0, so 2 is a divisor of 4058)
4058 / 3 = 1352.6666666667 (the remainder is 2, so 3 is not a divisor of 4058)
...
4058 / 4057 = 1.0002464875524 (the remainder is 1, so 4057 is not a divisor of 4058)
4058 / 4058 = 1 (the remainder is 0, so 4058 is a divisor of 4058)

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 4058 (i.e. 63.702433234532). 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 $\frac{N}{d} = D$ )

4058 / 1 = 4058 (the remainder is 0, so 1 and 4058 are divisors of 4058)
4058 / 2 = 2029 (the remainder is 0, so 2 and 2029 are divisors of 4058)
4058 / 3 = 1352.6666666667 (the remainder is 2, so 3 is not a divisor of 4058)
...
4058 / 62 = 65.451612903226 (the remainder is 28, so 62 is not a divisor of 4058)
4058 / 63 = 64.412698412698 (the remainder is 26, so 63 is not a divisor of 4058)