What are the divisors of 5654?

1, 2, 11, 22, 257, 514, 2827, 5654

There is a total of 8 positive divisors.
The sum of these divisors is 9288.
The arithmetic mean is 1161.

4 even divisors

2, 22, 514, 5654

4 odd divisors

1, 11, 257, 2827

How to compute the divisors of 5654?

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 5654 by each of the numbers from 1 to 5654 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)

5654 / 1 = 5654 (the remainder is 0, so 1 is a divisor of 5654)
5654 / 2 = 2827 (the remainder is 0, so 2 is a divisor of 5654)
5654 / 3 = 1884.6666666667 (the remainder is 2, so 3 is not a divisor of 5654)
...
5654 / 5653 = 1.0001768972227 (the remainder is 1, so 5653 is not a divisor of 5654)
5654 / 5654 = 1 (the remainder is 0, so 5654 is a divisor of 5654)

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 5654 (i.e. 75.19308478843). 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 $\frac{N}{d} = D$ )

5654 / 1 = 5654 (the remainder is 0, so 1 and 5654 are divisors of 5654)
5654 / 2 = 2827 (the remainder is 0, so 2 and 2827 are divisors of 5654)
5654 / 3 = 1884.6666666667 (the remainder is 2, so 3 is not a divisor of 5654)
...
5654 / 74 = 76.405405405405 (the remainder is 30, so 74 is not a divisor of 5654)
5654 / 75 = 75.386666666667 (the remainder is 29, so 75 is not a divisor of 5654)