What are the divisors of 5773?

1, 23, 251, 5773

There is a total of 4 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 1512.

4 odd divisors

1, 23, 251, 5773

How to compute the divisors of 5773?

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 5773 by each of the numbers from 1 to 5773 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)

5773 / 1 = 5773 (the remainder is 0, so 1 is a divisor of 5773)
5773 / 2 = 2886.5 (the remainder is 1, so 2 is not a divisor of 5773)
5773 / 3 = 1924.3333333333 (the remainder is 1, so 3 is not a divisor of 5773)
...
5773 / 5772 = 1.0001732501733 (the remainder is 1, so 5772 is not a divisor of 5773)
5773 / 5773 = 1 (the remainder is 0, so 5773 is a divisor of 5773)

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 5773 (i.e. 75.980260594447). 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 $\frac{N}{d} = D$ )

5773 / 1 = 5773 (the remainder is 0, so 1 and 5773 are divisors of 5773)
5773 / 2 = 2886.5 (the remainder is 1, so 2 is not a divisor of 5773)
5773 / 3 = 1924.3333333333 (the remainder is 1, so 3 is not a divisor of 5773)
...
5773 / 74 = 78.013513513514 (the remainder is 1, so 74 is not a divisor of 5773)
5773 / 75 = 76.973333333333 (the remainder is 73, so 75 is not a divisor of 5773)