What are the divisors of 5624?

1, 2, 4, 8, 19, 37, 38, 74, 76, 148, 152, 296, 703, 1406, 2812, 5624

There is a total of 16 positive divisors.
The sum of these divisors is 11400.
The arithmetic mean is 712.5.

12 even divisors

2, 4, 8, 38, 74, 76, 148, 152, 296, 1406, 2812, 5624

4 odd divisors

1, 19, 37, 703

How to compute the divisors of 5624?

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 5624 by each of the numbers from 1 to 5624 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)

5624 / 1 = 5624 (the remainder is 0, so 1 is a divisor of 5624)
5624 / 2 = 2812 (the remainder is 0, so 2 is a divisor of 5624)
5624 / 3 = 1874.6666666667 (the remainder is 2, so 3 is not a divisor of 5624)
...
5624 / 5623 = 1.0001778410101 (the remainder is 1, so 5623 is not a divisor of 5624)
5624 / 5624 = 1 (the remainder is 0, so 5624 is a divisor of 5624)

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 5624 (i.e. 74.993333037011). 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 $\frac{N}{d} = D$ )

5624 / 1 = 5624 (the remainder is 0, so 1 and 5624 are divisors of 5624)
5624 / 2 = 2812 (the remainder is 0, so 2 and 2812 are divisors of 5624)
5624 / 3 = 1874.6666666667 (the remainder is 2, so 3 is not a divisor of 5624)
...
5624 / 73 = 77.041095890411 (the remainder is 3, so 73 is not a divisor of 5624)
5624 / 74 = 76 (the remainder is 0, so 74 and 76 are divisors of 5624)