What are the divisors of 5338?

1, 2, 17, 34, 157, 314, 2669, 5338

There is a total of 8 positive divisors.
The sum of these divisors is 8532.
The arithmetic mean is 1066.5.

4 even divisors

2, 34, 314, 5338

4 odd divisors

1, 17, 157, 2669

How to compute the divisors of 5338?

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 5338 by each of the numbers from 1 to 5338 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)

5338 / 1 = 5338 (the remainder is 0, so 1 is a divisor of 5338)
5338 / 2 = 2669 (the remainder is 0, so 2 is a divisor of 5338)
5338 / 3 = 1779.3333333333 (the remainder is 1, so 3 is not a divisor of 5338)
...
5338 / 5337 = 1.0001873711823 (the remainder is 1, so 5337 is not a divisor of 5338)
5338 / 5338 = 1 (the remainder is 0, so 5338 is a divisor of 5338)

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 5338 (i.e. 73.061617830431). 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 $\frac{N}{d} = D$ )

5338 / 1 = 5338 (the remainder is 0, so 1 and 5338 are divisors of 5338)
5338 / 2 = 2669 (the remainder is 0, so 2 and 2669 are divisors of 5338)
5338 / 3 = 1779.3333333333 (the remainder is 1, so 3 is not a divisor of 5338)
...
5338 / 72 = 74.138888888889 (the remainder is 10, so 72 is not a divisor of 5338)
5338 / 73 = 73.123287671233 (the remainder is 9, so 73 is not a divisor of 5338)