What are the divisors of 2060?

1, 2, 4, 5, 10, 20, 103, 206, 412, 515, 1030, 2060

There is a total of 12 positive divisors.
The sum of these divisors is 4368.
The arithmetic mean is 364.

8 even divisors

2, 4, 10, 20, 206, 412, 1030, 2060

4 odd divisors

1, 5, 103, 515

How to compute the divisors of 2060?

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 2060 by each of the numbers from 1 to 2060 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)

2060 / 1 = 2060 (the remainder is 0, so 1 is a divisor of 2060)
2060 / 2 = 1030 (the remainder is 0, so 2 is a divisor of 2060)
2060 / 3 = 686.66666666667 (the remainder is 2, so 3 is not a divisor of 2060)
...
2060 / 2059 = 1.0004856726566 (the remainder is 1, so 2059 is not a divisor of 2060)
2060 / 2060 = 1 (the remainder is 0, so 2060 is a divisor of 2060)

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 2060 (i.e. 45.387222871641). 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 $\frac{N}{d} = D$ )

2060 / 1 = 2060 (the remainder is 0, so 1 and 2060 are divisors of 2060)
2060 / 2 = 1030 (the remainder is 0, so 2 and 1030 are divisors of 2060)
2060 / 3 = 686.66666666667 (the remainder is 2, so 3 is not a divisor of 2060)
...
2060 / 44 = 46.818181818182 (the remainder is 36, so 44 is not a divisor of 2060)
2060 / 45 = 45.777777777778 (the remainder is 35, so 45 is not a divisor of 2060)