What are the divisors of 2058?

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294, 343, 686, 1029, 2058

There is a total of 16 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 300.

8 even divisors

2, 6, 14, 42, 98, 294, 686, 2058

8 odd divisors

1, 3, 7, 21, 49, 147, 343, 1029

How to compute the divisors of 2058?

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 2058 by each of the numbers from 1 to 2058 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)

2058 / 1 = 2058 (the remainder is 0, so 1 is a divisor of 2058)
2058 / 2 = 1029 (the remainder is 0, so 2 is a divisor of 2058)
2058 / 3 = 686 (the remainder is 0, so 3 is a divisor of 2058)
...
2058 / 2057 = 1.0004861448712 (the remainder is 1, so 2057 is not a divisor of 2058)
2058 / 2058 = 1 (the remainder is 0, so 2058 is a divisor of 2058)

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 2058 (i.e. 45.365184888855). 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 $\frac{N}{d} = D$ )

2058 / 1 = 2058 (the remainder is 0, so 1 and 2058 are divisors of 2058)
2058 / 2 = 1029 (the remainder is 0, so 2 and 1029 are divisors of 2058)
2058 / 3 = 686 (the remainder is 0, so 3 and 686 are divisors of 2058)
...
2058 / 44 = 46.772727272727 (the remainder is 34, so 44 is not a divisor of 2058)
2058 / 45 = 45.733333333333 (the remainder is 33, so 45 is not a divisor of 2058)