What are the divisors of 5284?

1, 2, 4, 1321, 2642, 5284

There is a total of 6 positive divisors.
The sum of these divisors is 9254.
The arithmetic mean is 1542.3333333333.

4 even divisors

2, 4, 2642, 5284

2 odd divisors

1, 1321

How to compute the divisors of 5284?

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 5284 by each of the numbers from 1 to 5284 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)

5284 / 1 = 5284 (the remainder is 0, so 1 is a divisor of 5284)
5284 / 2 = 2642 (the remainder is 0, so 2 is a divisor of 5284)
5284 / 3 = 1761.3333333333 (the remainder is 1, so 3 is not a divisor of 5284)
...
5284 / 5283 = 1.0001892863903 (the remainder is 1, so 5283 is not a divisor of 5284)
5284 / 5284 = 1 (the remainder is 0, so 5284 is a divisor of 5284)

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 5284 (i.e. 72.691127381545). 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 $\frac{N}{d} = D$ )

5284 / 1 = 5284 (the remainder is 0, so 1 and 5284 are divisors of 5284)
5284 / 2 = 2642 (the remainder is 0, so 2 and 2642 are divisors of 5284)
5284 / 3 = 1761.3333333333 (the remainder is 1, so 3 is not a divisor of 5284)
...
5284 / 71 = 74.422535211268 (the remainder is 30, so 71 is not a divisor of 5284)
5284 / 72 = 73.388888888889 (the remainder is 28, so 72 is not a divisor of 5284)