What are the divisors of 5692?

1, 2, 4, 1423, 2846, 5692

There is a total of 6 positive divisors.
The sum of these divisors is 9968.
The arithmetic mean is 1661.3333333333.

4 even divisors

2, 4, 2846, 5692

2 odd divisors

1, 1423

How to compute the divisors of 5692?

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 5692 by each of the numbers from 1 to 5692 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)

5692 / 1 = 5692 (the remainder is 0, so 1 is a divisor of 5692)
5692 / 2 = 2846 (the remainder is 0, so 2 is a divisor of 5692)
5692 / 3 = 1897.3333333333 (the remainder is 1, so 3 is not a divisor of 5692)
...
5692 / 5691 = 1.0001757160429 (the remainder is 1, so 5691 is not a divisor of 5692)
5692 / 5692 = 1 (the remainder is 0, so 5692 is a divisor of 5692)

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 5692 (i.e. 75.44534445544). 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 $\frac{N}{d} = D$ )

5692 / 1 = 5692 (the remainder is 0, so 1 and 5692 are divisors of 5692)
5692 / 2 = 2846 (the remainder is 0, so 2 and 2846 are divisors of 5692)
5692 / 3 = 1897.3333333333 (the remainder is 1, so 3 is not a divisor of 5692)
...
5692 / 74 = 76.918918918919 (the remainder is 68, so 74 is not a divisor of 5692)
5692 / 75 = 75.893333333333 (the remainder is 67, so 75 is not a divisor of 5692)