What are the divisors of 5592?

1, 2, 3, 4, 6, 8, 12, 24, 233, 466, 699, 932, 1398, 1864, 2796, 5592

There is a total of 16 positive divisors.
The sum of these divisors is 14040.
The arithmetic mean is 877.5.

12 even divisors

2, 4, 6, 8, 12, 24, 466, 932, 1398, 1864, 2796, 5592

4 odd divisors

1, 3, 233, 699

How to compute the divisors of 5592?

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 5592 by each of the numbers from 1 to 5592 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)

5592 / 1 = 5592 (the remainder is 0, so 1 is a divisor of 5592)
5592 / 2 = 2796 (the remainder is 0, so 2 is a divisor of 5592)
5592 / 3 = 1864 (the remainder is 0, so 3 is a divisor of 5592)
...
5592 / 5591 = 1.0001788588803 (the remainder is 1, so 5591 is not a divisor of 5592)
5592 / 5592 = 1 (the remainder is 0, so 5592 is a divisor of 5592)

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 5592 (i.e. 74.77967638336). 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 $\frac{N}{d} = D$ )

5592 / 1 = 5592 (the remainder is 0, so 1 and 5592 are divisors of 5592)
5592 / 2 = 2796 (the remainder is 0, so 2 and 2796 are divisors of 5592)
5592 / 3 = 1864 (the remainder is 0, so 3 and 1864 are divisors of 5592)
...
5592 / 73 = 76.602739726027 (the remainder is 44, so 73 is not a divisor of 5592)
5592 / 74 = 75.567567567568 (the remainder is 42, so 74 is not a divisor of 5592)