What are the divisors of 5556?

1, 2, 3, 4, 6, 12, 463, 926, 1389, 1852, 2778, 5556

There is a total of 12 positive divisors.
The sum of these divisors is 12992.
The arithmetic mean is 1082.6666666667.

8 even divisors

2, 4, 6, 12, 926, 1852, 2778, 5556

4 odd divisors

1, 3, 463, 1389

How to compute the divisors of 5556?

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 5556 by each of the numbers from 1 to 5556 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)

5556 / 1 = 5556 (the remainder is 0, so 1 is a divisor of 5556)
5556 / 2 = 2778 (the remainder is 0, so 2 is a divisor of 5556)
5556 / 3 = 1852 (the remainder is 0, so 3 is a divisor of 5556)
...
5556 / 5555 = 1.0001800180018 (the remainder is 1, so 5555 is not a divisor of 5556)
5556 / 5556 = 1 (the remainder is 0, so 5556 is a divisor of 5556)

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 5556 (i.e. 74.538580614337). 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 $\frac{N}{d} = D$ )

5556 / 1 = 5556 (the remainder is 0, so 1 and 5556 are divisors of 5556)
5556 / 2 = 2778 (the remainder is 0, so 2 and 2778 are divisors of 5556)
5556 / 3 = 1852 (the remainder is 0, so 3 and 1852 are divisors of 5556)
...
5556 / 73 = 76.109589041096 (the remainder is 8, so 73 is not a divisor of 5556)
5556 / 74 = 75.081081081081 (the remainder is 6, so 74 is not a divisor of 5556)