What are the divisors of 5757?

1, 3, 19, 57, 101, 303, 1919, 5757

There is a total of 8 positive divisors.
The sum of these divisors is 8160.
The arithmetic mean is 1020.

8 odd divisors

1, 3, 19, 57, 101, 303, 1919, 5757

How to compute the divisors of 5757?

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 5757 by each of the numbers from 1 to 5757 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)

5757 / 1 = 5757 (the remainder is 0, so 1 is a divisor of 5757)
5757 / 2 = 2878.5 (the remainder is 1, so 2 is not a divisor of 5757)
5757 / 3 = 1919 (the remainder is 0, so 3 is a divisor of 5757)
...
5757 / 5756 = 1.0001737317582 (the remainder is 1, so 5756 is not a divisor of 5757)
5757 / 5757 = 1 (the remainder is 0, so 5757 is a divisor of 5757)

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 5757 (i.e. 75.874897034527). 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 $\frac{N}{d} = D$ )

5757 / 1 = 5757 (the remainder is 0, so 1 and 5757 are divisors of 5757)
5757 / 2 = 2878.5 (the remainder is 1, so 2 is not a divisor of 5757)
5757 / 3 = 1919 (the remainder is 0, so 3 and 1919 are divisors of 5757)
...
5757 / 74 = 77.797297297297 (the remainder is 59, so 74 is not a divisor of 5757)
5757 / 75 = 76.76 (the remainder is 57, so 75 is not a divisor of 5757)