What are the divisors of 5362?

1, 2, 7, 14, 383, 766, 2681, 5362

There is a total of 8 positive divisors.
The sum of these divisors is 9216.
The arithmetic mean is 1152.

4 even divisors

2, 14, 766, 5362

4 odd divisors

1, 7, 383, 2681

How to compute the divisors of 5362?

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 5362 by each of the numbers from 1 to 5362 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)

5362 / 1 = 5362 (the remainder is 0, so 1 is a divisor of 5362)
5362 / 2 = 2681 (the remainder is 0, so 2 is a divisor of 5362)
5362 / 3 = 1787.3333333333 (the remainder is 1, so 3 is not a divisor of 5362)
...
5362 / 5361 = 1.0001865323634 (the remainder is 1, so 5361 is not a divisor of 5362)
5362 / 5362 = 1 (the remainder is 0, so 5362 is a divisor of 5362)

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 5362 (i.e. 73.225678556091). 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 $\frac{N}{d} = D$ )

5362 / 1 = 5362 (the remainder is 0, so 1 and 5362 are divisors of 5362)
5362 / 2 = 2681 (the remainder is 0, so 2 and 2681 are divisors of 5362)
5362 / 3 = 1787.3333333333 (the remainder is 1, so 3 is not a divisor of 5362)
...
5362 / 72 = 74.472222222222 (the remainder is 34, so 72 is not a divisor of 5362)
5362 / 73 = 73.452054794521 (the remainder is 33, so 73 is not a divisor of 5362)