What are the divisors of 5604?

1, 2, 3, 4, 6, 12, 467, 934, 1401, 1868, 2802, 5604

There is a total of 12 positive divisors.
The sum of these divisors is 13104.
The arithmetic mean is 1092.

8 even divisors

2, 4, 6, 12, 934, 1868, 2802, 5604

4 odd divisors

1, 3, 467, 1401

How to compute the divisors of 5604?

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 5604 by each of the numbers from 1 to 5604 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)

5604 / 1 = 5604 (the remainder is 0, so 1 is a divisor of 5604)
5604 / 2 = 2802 (the remainder is 0, so 2 is a divisor of 5604)
5604 / 3 = 1868 (the remainder is 0, so 3 is a divisor of 5604)
...
5604 / 5603 = 1.0001784758165 (the remainder is 1, so 5603 is not a divisor of 5604)
5604 / 5604 = 1 (the remainder is 0, so 5604 is a divisor of 5604)

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 5604 (i.e. 74.859869088852). 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 $\frac{N}{d} = D$ )

5604 / 1 = 5604 (the remainder is 0, so 1 and 5604 are divisors of 5604)
5604 / 2 = 2802 (the remainder is 0, so 2 and 2802 are divisors of 5604)
5604 / 3 = 1868 (the remainder is 0, so 3 and 1868 are divisors of 5604)
...
5604 / 73 = 76.767123287671 (the remainder is 56, so 73 is not a divisor of 5604)
5604 / 74 = 75.72972972973 (the remainder is 54, so 74 is not a divisor of 5604)