What are the divisors of 1058?

1, 2, 23, 46, 529, 1058

There is a total of 6 positive divisors.
The sum of these divisors is 1659.
The arithmetic mean is 276.5.

3 even divisors

2, 46, 1058

3 odd divisors

1, 23, 529

How to compute the divisors of 1058?

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 1058 by each of the numbers from 1 to 1058 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)

1058 / 1 = 1058 (the remainder is 0, so 1 is a divisor of 1058)
1058 / 2 = 529 (the remainder is 0, so 2 is a divisor of 1058)
1058 / 3 = 352.66666666667 (the remainder is 2, so 3 is not a divisor of 1058)
...
1058 / 1057 = 1.0009460737938 (the remainder is 1, so 1057 is not a divisor of 1058)
1058 / 1058 = 1 (the remainder is 0, so 1058 is a divisor of 1058)

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 1058 (i.e. 32.526911934581). 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 $\frac{N}{d} = D$ )

1058 / 1 = 1058 (the remainder is 0, so 1 and 1058 are divisors of 1058)
1058 / 2 = 529 (the remainder is 0, so 2 and 529 are divisors of 1058)
1058 / 3 = 352.66666666667 (the remainder is 2, so 3 is not a divisor of 1058)
...
1058 / 31 = 34.129032258065 (the remainder is 4, so 31 is not a divisor of 1058)
1058 / 32 = 33.0625 (the remainder is 2, so 32 is not a divisor of 1058)