What are the divisors of 5644?

1, 2, 4, 17, 34, 68, 83, 166, 332, 1411, 2822, 5644

There is a total of 12 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 882.

8 even divisors

2, 4, 34, 68, 166, 332, 2822, 5644

4 odd divisors

1, 17, 83, 1411

How to compute the divisors of 5644?

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 5644 by each of the numbers from 1 to 5644 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)

5644 / 1 = 5644 (the remainder is 0, so 1 is a divisor of 5644)
5644 / 2 = 2822 (the remainder is 0, so 2 is a divisor of 5644)
5644 / 3 = 1881.3333333333 (the remainder is 1, so 3 is not a divisor of 5644)
...
5644 / 5643 = 1.0001772107035 (the remainder is 1, so 5643 is not a divisor of 5644)
5644 / 5644 = 1 (the remainder is 0, so 5644 is a divisor of 5644)

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 5644 (i.e. 75.126559883972). 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 $\frac{N}{d} = D$ )

5644 / 1 = 5644 (the remainder is 0, so 1 and 5644 are divisors of 5644)
5644 / 2 = 2822 (the remainder is 0, so 2 and 2822 are divisors of 5644)
5644 / 3 = 1881.3333333333 (the remainder is 1, so 3 is not a divisor of 5644)
...
5644 / 74 = 76.27027027027 (the remainder is 20, so 74 is not a divisor of 5644)
5644 / 75 = 75.253333333333 (the remainder is 19, so 75 is not a divisor of 5644)