What are the divisors of 5734?

1, 2, 47, 61, 94, 122, 2867, 5734

There is a total of 8 positive divisors.
The sum of these divisors is 8928.
The arithmetic mean is 1116.

4 even divisors

2, 94, 122, 5734

4 odd divisors

1, 47, 61, 2867

How to compute the divisors of 5734?

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 5734 by each of the numbers from 1 to 5734 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)

5734 / 1 = 5734 (the remainder is 0, so 1 is a divisor of 5734)
5734 / 2 = 2867 (the remainder is 0, so 2 is a divisor of 5734)
5734 / 3 = 1911.3333333333 (the remainder is 1, so 3 is not a divisor of 5734)
...
5734 / 5733 = 1.0001744287459 (the remainder is 1, so 5733 is not a divisor of 5734)
5734 / 5734 = 1 (the remainder is 0, so 5734 is a divisor of 5734)

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 5734 (i.e. 75.72318007057). 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 $\frac{N}{d} = D$ )

5734 / 1 = 5734 (the remainder is 0, so 1 and 5734 are divisors of 5734)
5734 / 2 = 2867 (the remainder is 0, so 2 and 2867 are divisors of 5734)
5734 / 3 = 1911.3333333333 (the remainder is 1, so 3 is not a divisor of 5734)
...
5734 / 74 = 77.486486486486 (the remainder is 36, so 74 is not a divisor of 5734)
5734 / 75 = 76.453333333333 (the remainder is 34, so 75 is not a divisor of 5734)