What are the divisors of 5780?

1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 289, 340, 578, 1156, 1445, 2890, 5780

There is a total of 18 positive divisors.
The sum of these divisors is 12894.
The arithmetic mean is 716.33333333333.

12 even divisors

2, 4, 10, 20, 34, 68, 170, 340, 578, 1156, 2890, 5780

6 odd divisors

1, 5, 17, 85, 289, 1445

How to compute the divisors of 5780?

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 5780 by each of the numbers from 1 to 5780 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)

5780 / 1 = 5780 (the remainder is 0, so 1 is a divisor of 5780)
5780 / 2 = 2890 (the remainder is 0, so 2 is a divisor of 5780)
5780 / 3 = 1926.6666666667 (the remainder is 2, so 3 is not a divisor of 5780)
...
5780 / 5779 = 1.0001730403184 (the remainder is 1, so 5779 is not a divisor of 5780)
5780 / 5780 = 1 (the remainder is 0, so 5780 is a divisor of 5780)

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 5780 (i.e. 76.026311234993). 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 $\frac{N}{d} = D$ )

5780 / 1 = 5780 (the remainder is 0, so 1 and 5780 are divisors of 5780)
5780 / 2 = 2890 (the remainder is 0, so 2 and 2890 are divisors of 5780)
5780 / 3 = 1926.6666666667 (the remainder is 2, so 3 is not a divisor of 5780)
...
5780 / 75 = 77.066666666667 (the remainder is 5, so 75 is not a divisor of 5780)
5780 / 76 = 76.052631578947 (the remainder is 4, so 76 is not a divisor of 5780)