What are the divisors of 5384?

1, 2, 4, 8, 673, 1346, 2692, 5384

There is a total of 8 positive divisors.
The sum of these divisors is 10110.
The arithmetic mean is 1263.75.

6 even divisors

2, 4, 8, 1346, 2692, 5384

2 odd divisors

1, 673

How to compute the divisors of 5384?

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 5384 by each of the numbers from 1 to 5384 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)

5384 / 1 = 5384 (the remainder is 0, so 1 is a divisor of 5384)
5384 / 2 = 2692 (the remainder is 0, so 2 is a divisor of 5384)
5384 / 3 = 1794.6666666667 (the remainder is 2, so 3 is not a divisor of 5384)
...
5384 / 5383 = 1.0001857700167 (the remainder is 1, so 5383 is not a divisor of 5384)
5384 / 5384 = 1 (the remainder is 0, so 5384 is a divisor of 5384)

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 5384 (i.e. 73.375745311377). 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 $\frac{N}{d} = D$ )

5384 / 1 = 5384 (the remainder is 0, so 1 and 5384 are divisors of 5384)
5384 / 2 = 2692 (the remainder is 0, so 2 and 2692 are divisors of 5384)
5384 / 3 = 1794.6666666667 (the remainder is 2, so 3 is not a divisor of 5384)
...
5384 / 72 = 74.777777777778 (the remainder is 56, so 72 is not a divisor of 5384)
5384 / 73 = 73.753424657534 (the remainder is 55, so 73 is not a divisor of 5384)