What are the divisors of 5770?

1, 2, 5, 10, 577, 1154, 2885, 5770

There is a total of 8 positive divisors.
The sum of these divisors is 10404.
The arithmetic mean is 1300.5.

4 even divisors

2, 10, 1154, 5770

4 odd divisors

1, 5, 577, 2885

How to compute the divisors of 5770?

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 5770 by each of the numbers from 1 to 5770 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)

5770 / 1 = 5770 (the remainder is 0, so 1 is a divisor of 5770)
5770 / 2 = 2885 (the remainder is 0, so 2 is a divisor of 5770)
5770 / 3 = 1923.3333333333 (the remainder is 1, so 3 is not a divisor of 5770)
...
5770 / 5769 = 1.0001733402669 (the remainder is 1, so 5769 is not a divisor of 5770)
5770 / 5770 = 1 (the remainder is 0, so 5770 is a divisor of 5770)

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 5770 (i.e. 75.960516059332). 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 $\frac{N}{d} = D$ )

5770 / 1 = 5770 (the remainder is 0, so 1 and 5770 are divisors of 5770)
5770 / 2 = 2885 (the remainder is 0, so 2 and 2885 are divisors of 5770)
5770 / 3 = 1923.3333333333 (the remainder is 1, so 3 is not a divisor of 5770)
...
5770 / 74 = 77.972972972973 (the remainder is 72, so 74 is not a divisor of 5770)
5770 / 75 = 76.933333333333 (the remainder is 70, so 75 is not a divisor of 5770)