What are the divisors of 5697?

1, 3, 9, 27, 211, 633, 1899, 5697

There is a total of 8 positive divisors.
The sum of these divisors is 8480.
The arithmetic mean is 1060.

8 odd divisors

1, 3, 9, 27, 211, 633, 1899, 5697

How to compute the divisors of 5697?

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 5697 by each of the numbers from 1 to 5697 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)

5697 / 1 = 5697 (the remainder is 0, so 1 is a divisor of 5697)
5697 / 2 = 2848.5 (the remainder is 1, so 2 is not a divisor of 5697)
5697 / 3 = 1899 (the remainder is 0, so 3 is a divisor of 5697)
...
5697 / 5696 = 1.0001755617978 (the remainder is 1, so 5696 is not a divisor of 5697)
5697 / 5697 = 1 (the remainder is 0, so 5697 is a divisor of 5697)

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 5697 (i.e. 75.478473752455). 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 $\frac{N}{d} = D$ )

5697 / 1 = 5697 (the remainder is 0, so 1 and 5697 are divisors of 5697)
5697 / 2 = 2848.5 (the remainder is 1, so 2 is not a divisor of 5697)
5697 / 3 = 1899 (the remainder is 0, so 3 and 1899 are divisors of 5697)
...
5697 / 74 = 76.986486486486 (the remainder is 73, so 74 is not a divisor of 5697)
5697 / 75 = 75.96 (the remainder is 72, so 75 is not a divisor of 5697)