What are the divisors of 5753?

1, 11, 523, 5753

There is a total of 4 positive divisors.
The sum of these divisors is 6288.
The arithmetic mean is 1572.

4 odd divisors

1, 11, 523, 5753

How to compute the divisors of 5753?

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 5753 by each of the numbers from 1 to 5753 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)

5753 / 1 = 5753 (the remainder is 0, so 1 is a divisor of 5753)
5753 / 2 = 2876.5 (the remainder is 1, so 2 is not a divisor of 5753)
5753 / 3 = 1917.6666666667 (the remainder is 2, so 3 is not a divisor of 5753)
...
5753 / 5752 = 1.000173852573 (the remainder is 1, so 5752 is not a divisor of 5753)
5753 / 5753 = 1 (the remainder is 0, so 5753 is a divisor of 5753)

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 5753 (i.e. 75.848533275206). 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 $\frac{N}{d} = D$ )

5753 / 1 = 5753 (the remainder is 0, so 1 and 5753 are divisors of 5753)
5753 / 2 = 2876.5 (the remainder is 1, so 2 is not a divisor of 5753)
5753 / 3 = 1917.6666666667 (the remainder is 2, so 3 is not a divisor of 5753)
...
5753 / 74 = 77.743243243243 (the remainder is 55, so 74 is not a divisor of 5753)
5753 / 75 = 76.706666666667 (the remainder is 53, so 75 is not a divisor of 5753)