What are the divisors of 5772?

1, 2, 3, 4, 6, 12, 13, 26, 37, 39, 52, 74, 78, 111, 148, 156, 222, 444, 481, 962, 1443, 1924, 2886, 5772

There is a total of 24 positive divisors.
The sum of these divisors is 14896.
The arithmetic mean is 620.66666666667.

16 even divisors

2, 4, 6, 12, 26, 52, 74, 78, 148, 156, 222, 444, 962, 1924, 2886, 5772

8 odd divisors

1, 3, 13, 37, 39, 111, 481, 1443

How to compute the divisors of 5772?

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 5772 by each of the numbers from 1 to 5772 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)

5772 / 1 = 5772 (the remainder is 0, so 1 is a divisor of 5772)
5772 / 2 = 2886 (the remainder is 0, so 2 is a divisor of 5772)
5772 / 3 = 1924 (the remainder is 0, so 3 is a divisor of 5772)
...
5772 / 5771 = 1.0001732801941 (the remainder is 1, so 5771 is not a divisor of 5772)
5772 / 5772 = 1 (the remainder is 0, so 5772 is a divisor of 5772)

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 5772 (i.e. 75.97367965289). 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 $\frac{N}{d} = D$ )

5772 / 1 = 5772 (the remainder is 0, so 1 and 5772 are divisors of 5772)
5772 / 2 = 2886 (the remainder is 0, so 2 and 2886 are divisors of 5772)
5772 / 3 = 1924 (the remainder is 0, so 3 and 1924 are divisors of 5772)
...
5772 / 74 = 78 (the remainder is 0, so 74 and 78 are divisors of 5772)
5772 / 75 = 76.96 (the remainder is 72, so 75 is not a divisor of 5772)