What are the divisors of 5755?

1, 5, 1151, 5755

There is a total of 4 positive divisors.
The sum of these divisors is 6912.
The arithmetic mean is 1728.

4 odd divisors

1, 5, 1151, 5755

How to compute the divisors of 5755?

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 5755 by each of the numbers from 1 to 5755 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)

5755 / 1 = 5755 (the remainder is 0, so 1 is a divisor of 5755)
5755 / 2 = 2877.5 (the remainder is 1, so 2 is not a divisor of 5755)
5755 / 3 = 1918.3333333333 (the remainder is 1, so 3 is not a divisor of 5755)
...
5755 / 5754 = 1.0001737921446 (the remainder is 1, so 5754 is not a divisor of 5755)
5755 / 5755 = 1 (the remainder is 0, so 5755 is a divisor of 5755)

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 5755 (i.e. 75.861716300121). 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 $\frac{N}{d} = D$ )

5755 / 1 = 5755 (the remainder is 0, so 1 and 5755 are divisors of 5755)
5755 / 2 = 2877.5 (the remainder is 1, so 2 is not a divisor of 5755)
5755 / 3 = 1918.3333333333 (the remainder is 1, so 3 is not a divisor of 5755)
...
5755 / 74 = 77.77027027027 (the remainder is 57, so 74 is not a divisor of 5755)
5755 / 75 = 76.733333333333 (the remainder is 55, so 75 is not a divisor of 5755)