What are the divisors of 5784?

1, 2, 3, 4, 6, 8, 12, 24, 241, 482, 723, 964, 1446, 1928, 2892, 5784

There is a total of 16 positive divisors.
The sum of these divisors is 14520.
The arithmetic mean is 907.5.

12 even divisors

2, 4, 6, 8, 12, 24, 482, 964, 1446, 1928, 2892, 5784

4 odd divisors

1, 3, 241, 723

How to compute the divisors of 5784?

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 5784 by each of the numbers from 1 to 5784 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)

5784 / 1 = 5784 (the remainder is 0, so 1 is a divisor of 5784)
5784 / 2 = 2892 (the remainder is 0, so 2 is a divisor of 5784)
5784 / 3 = 1928 (the remainder is 0, so 3 is a divisor of 5784)
...
5784 / 5783 = 1.0001729206294 (the remainder is 1, so 5783 is not a divisor of 5784)
5784 / 5784 = 1 (the remainder is 0, so 5784 is a divisor of 5784)

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 5784 (i.e. 76.052613367326). 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 $\frac{N}{d} = D$ )

5784 / 1 = 5784 (the remainder is 0, so 1 and 5784 are divisors of 5784)
5784 / 2 = 2892 (the remainder is 0, so 2 and 2892 are divisors of 5784)
5784 / 3 = 1928 (the remainder is 0, so 3 and 1928 are divisors of 5784)
...
5784 / 75 = 77.12 (the remainder is 9, so 75 is not a divisor of 5784)
5784 / 76 = 76.105263157895 (the remainder is 8, so 76 is not a divisor of 5784)