What are the divisors of 5774?

1, 2, 2887, 5774

There is a total of 4 positive divisors.
The sum of these divisors is 8664.
The arithmetic mean is 2166.

2 even divisors

2, 5774

2 odd divisors

1, 2887

How to compute the divisors of 5774?

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 5774 by each of the numbers from 1 to 5774 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)

5774 / 1 = 5774 (the remainder is 0, so 1 is a divisor of 5774)
5774 / 2 = 2887 (the remainder is 0, so 2 is a divisor of 5774)
5774 / 3 = 1924.6666666667 (the remainder is 2, so 3 is not a divisor of 5774)
...
5774 / 5773 = 1.0001732201628 (the remainder is 1, so 5773 is not a divisor of 5774)
5774 / 5774 = 1 (the remainder is 0, so 5774 is a divisor of 5774)

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 5774 (i.e. 75.986840966051). 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 $\frac{N}{d} = D$ )

5774 / 1 = 5774 (the remainder is 0, so 1 and 5774 are divisors of 5774)
5774 / 2 = 2887 (the remainder is 0, so 2 and 2887 are divisors of 5774)
5774 / 3 = 1924.6666666667 (the remainder is 2, so 3 is not a divisor of 5774)
...
5774 / 74 = 78.027027027027 (the remainder is 2, so 74 is not a divisor of 5774)
5774 / 75 = 76.986666666667 (the remainder is 74, so 75 is not a divisor of 5774)