What are the divisors of 5834?

1, 2, 2917, 5834

There is a total of 4 positive divisors.
The sum of these divisors is 8754.
The arithmetic mean is 2188.5.

2 even divisors

2, 5834

2 odd divisors

1, 2917

How to compute the divisors of 5834?

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 5834 by each of the numbers from 1 to 5834 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)

5834 / 1 = 5834 (the remainder is 0, so 1 is a divisor of 5834)
5834 / 2 = 2917 (the remainder is 0, so 2 is a divisor of 5834)
5834 / 3 = 1944.6666666667 (the remainder is 2, so 3 is not a divisor of 5834)
...
5834 / 5833 = 1.0001714383679 (the remainder is 1, so 5833 is not a divisor of 5834)
5834 / 5834 = 1 (the remainder is 0, so 5834 is a divisor of 5834)

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 5834 (i.e. 76.380625815713). 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 $\frac{N}{d} = D$ )

5834 / 1 = 5834 (the remainder is 0, so 1 and 5834 are divisors of 5834)
5834 / 2 = 2917 (the remainder is 0, so 2 and 2917 are divisors of 5834)
5834 / 3 = 1944.6666666667 (the remainder is 2, so 3 is not a divisor of 5834)
...
5834 / 75 = 77.786666666667 (the remainder is 59, so 75 is not a divisor of 5834)
5834 / 76 = 76.763157894737 (the remainder is 58, so 76 is not a divisor of 5834)