What are the divisors of 5634?

1, 2, 3, 6, 9, 18, 313, 626, 939, 1878, 2817, 5634

There is a total of 12 positive divisors.
The sum of these divisors is 12246.
The arithmetic mean is 1020.5.

6 even divisors

2, 6, 18, 626, 1878, 5634

6 odd divisors

1, 3, 9, 313, 939, 2817

How to compute the divisors of 5634?

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 5634 by each of the numbers from 1 to 5634 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)

5634 / 1 = 5634 (the remainder is 0, so 1 is a divisor of 5634)
5634 / 2 = 2817 (the remainder is 0, so 2 is a divisor of 5634)
5634 / 3 = 1878 (the remainder is 0, so 3 is a divisor of 5634)
...
5634 / 5633 = 1.0001775252974 (the remainder is 1, so 5633 is not a divisor of 5634)
5634 / 5634 = 1 (the remainder is 0, so 5634 is a divisor of 5634)

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 5634 (i.e. 75.059976019181). 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 $\frac{N}{d} = D$ )

5634 / 1 = 5634 (the remainder is 0, so 1 and 5634 are divisors of 5634)
5634 / 2 = 2817 (the remainder is 0, so 2 and 2817 are divisors of 5634)
5634 / 3 = 1878 (the remainder is 0, so 3 and 1878 are divisors of 5634)
...
5634 / 74 = 76.135135135135 (the remainder is 10, so 74 is not a divisor of 5634)
5634 / 75 = 75.12 (the remainder is 9, so 75 is not a divisor of 5634)