What are the divisors of 5864?

1, 2, 4, 8, 733, 1466, 2932, 5864

There is a total of 8 positive divisors.
The sum of these divisors is 11010.
The arithmetic mean is 1376.25.

6 even divisors

2, 4, 8, 1466, 2932, 5864

2 odd divisors

1, 733

How to compute the divisors of 5864?

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 5864 by each of the numbers from 1 to 5864 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)

5864 / 1 = 5864 (the remainder is 0, so 1 is a divisor of 5864)
5864 / 2 = 2932 (the remainder is 0, so 2 is a divisor of 5864)
5864 / 3 = 1954.6666666667 (the remainder is 2, so 3 is not a divisor of 5864)
...
5864 / 5863 = 1.0001705611462 (the remainder is 1, so 5863 is not a divisor of 5864)
5864 / 5864 = 1 (the remainder is 0, so 5864 is a divisor of 5864)

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 5864 (i.e. 76.576758876307). 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 $\frac{N}{d} = D$ )

5864 / 1 = 5864 (the remainder is 0, so 1 and 5864 are divisors of 5864)
5864 / 2 = 2932 (the remainder is 0, so 2 and 2932 are divisors of 5864)
5864 / 3 = 1954.6666666667 (the remainder is 2, so 3 is not a divisor of 5864)
...
5864 / 75 = 78.186666666667 (the remainder is 14, so 75 is not a divisor of 5864)
5864 / 76 = 77.157894736842 (the remainder is 12, so 76 is not a divisor of 5864)