What are the divisors of 5532?

1, 2, 3, 4, 6, 12, 461, 922, 1383, 1844, 2766, 5532

There is a total of 12 positive divisors.
The sum of these divisors is 12936.
The arithmetic mean is 1078.

8 even divisors

2, 4, 6, 12, 922, 1844, 2766, 5532

4 odd divisors

1, 3, 461, 1383

How to compute the divisors of 5532?

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 5532 by each of the numbers from 1 to 5532 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)

5532 / 1 = 5532 (the remainder is 0, so 1 is a divisor of 5532)
5532 / 2 = 2766 (the remainder is 0, so 2 is a divisor of 5532)
5532 / 3 = 1844 (the remainder is 0, so 3 is a divisor of 5532)
...
5532 / 5531 = 1.0001807991322 (the remainder is 1, so 5531 is not a divisor of 5532)
5532 / 5532 = 1 (the remainder is 0, so 5532 is a divisor of 5532)

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 5532 (i.e. 74.377415927148). 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 $\frac{N}{d} = D$ )

5532 / 1 = 5532 (the remainder is 0, so 1 and 5532 are divisors of 5532)
5532 / 2 = 2766 (the remainder is 0, so 2 and 2766 are divisors of 5532)
5532 / 3 = 1844 (the remainder is 0, so 3 and 1844 are divisors of 5532)
...
5532 / 73 = 75.780821917808 (the remainder is 57, so 73 is not a divisor of 5532)
5532 / 74 = 74.756756756757 (the remainder is 56, so 74 is not a divisor of 5532)