What are the divisors of 5928?

1, 2, 3, 4, 6, 8, 12, 13, 19, 24, 26, 38, 39, 52, 57, 76, 78, 104, 114, 152, 156, 228, 247, 312, 456, 494, 741, 988, 1482, 1976, 2964, 5928

There is a total of 32 positive divisors.
The sum of these divisors is 16800.
The arithmetic mean is 525.

24 even divisors

2, 4, 6, 8, 12, 24, 26, 38, 52, 76, 78, 104, 114, 152, 156, 228, 312, 456, 494, 988, 1482, 1976, 2964, 5928

8 odd divisors

1, 3, 13, 19, 39, 57, 247, 741

How to compute the divisors of 5928?

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 5928 by each of the numbers from 1 to 5928 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)

5928 / 1 = 5928 (the remainder is 0, so 1 is a divisor of 5928)
5928 / 2 = 2964 (the remainder is 0, so 2 is a divisor of 5928)
5928 / 3 = 1976 (the remainder is 0, so 3 is a divisor of 5928)
...
5928 / 5927 = 1.0001687194196 (the remainder is 1, so 5927 is not a divisor of 5928)
5928 / 5928 = 1 (the remainder is 0, so 5928 is a divisor of 5928)

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 5928 (i.e. 76.993506219681). 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 $\frac{N}{d} = D$ )

5928 / 1 = 5928 (the remainder is 0, so 1 and 5928 are divisors of 5928)
5928 / 2 = 2964 (the remainder is 0, so 2 and 2964 are divisors of 5928)
5928 / 3 = 1976 (the remainder is 0, so 3 and 1976 are divisors of 5928)
...
5928 / 75 = 79.04 (the remainder is 3, so 75 is not a divisor of 5928)
5928 / 76 = 78 (the remainder is 0, so 76 and 78 are divisors of 5928)