What are the divisors of 5437?

1, 5437

There is a total of 2 positive divisors.
The sum of these divisors is 5438.
The arithmetic mean is 2719.

2 odd divisors

1, 5437

How to compute the divisors of 5437?

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 5437 by each of the numbers from 1 to 5437 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)

5437 / 1 = 5437 (the remainder is 0, so 1 is a divisor of 5437)
5437 / 2 = 2718.5 (the remainder is 1, so 2 is not a divisor of 5437)
5437 / 3 = 1812.3333333333 (the remainder is 1, so 3 is not a divisor of 5437)
...
5437 / 5436 = 1.0001839587932 (the remainder is 1, so 5436 is not a divisor of 5437)
5437 / 5437 = 1 (the remainder is 0, so 5437 is a divisor of 5437)

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 5437 (i.e. 73.736015623303). 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 $\frac{N}{d} = D$ )

5437 / 1 = 5437 (the remainder is 0, so 1 and 5437 are divisors of 5437)
5437 / 2 = 2718.5 (the remainder is 1, so 2 is not a divisor of 5437)
5437 / 3 = 1812.3333333333 (the remainder is 1, so 3 is not a divisor of 5437)
...
5437 / 72 = 75.513888888889 (the remainder is 37, so 72 is not a divisor of 5437)
5437 / 73 = 74.479452054795 (the remainder is 35, so 73 is not a divisor of 5437)