What are the divisors of 5464?

1, 2, 4, 8, 683, 1366, 2732, 5464

There is a total of 8 positive divisors.
The sum of these divisors is 10260.
The arithmetic mean is 1282.5.

6 even divisors

2, 4, 8, 1366, 2732, 5464

2 odd divisors

1, 683

How to compute the divisors of 5464?

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 5464 by each of the numbers from 1 to 5464 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)

5464 / 1 = 5464 (the remainder is 0, so 1 is a divisor of 5464)
5464 / 2 = 2732 (the remainder is 0, so 2 is a divisor of 5464)
5464 / 3 = 1821.3333333333 (the remainder is 1, so 3 is not a divisor of 5464)
...
5464 / 5463 = 1.0001830496064 (the remainder is 1, so 5463 is not a divisor of 5464)
5464 / 5464 = 1 (the remainder is 0, so 5464 is a divisor of 5464)

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 5464 (i.e. 73.918874450305). 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 $\frac{N}{d} = D$ )

5464 / 1 = 5464 (the remainder is 0, so 1 and 5464 are divisors of 5464)
5464 / 2 = 2732 (the remainder is 0, so 2 and 2732 are divisors of 5464)
5464 / 3 = 1821.3333333333 (the remainder is 1, so 3 is not a divisor of 5464)
...
5464 / 72 = 75.888888888889 (the remainder is 64, so 72 is not a divisor of 5464)
5464 / 73 = 74.849315068493 (the remainder is 62, so 73 is not a divisor of 5464)