What are the divisors of 5537?

1, 7, 49, 113, 791, 5537

There is a total of 6 positive divisors.
The sum of these divisors is 6498.
The arithmetic mean is 1083.

6 odd divisors

1, 7, 49, 113, 791, 5537

How to compute the divisors of 5537?

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 5537 by each of the numbers from 1 to 5537 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)

5537 / 1 = 5537 (the remainder is 0, so 1 is a divisor of 5537)
5537 / 2 = 2768.5 (the remainder is 1, so 2 is not a divisor of 5537)
5537 / 3 = 1845.6666666667 (the remainder is 2, so 3 is not a divisor of 5537)
...
5537 / 5536 = 1.0001806358382 (the remainder is 1, so 5536 is not a divisor of 5537)
5537 / 5537 = 1 (the remainder is 0, so 5537 is a divisor of 5537)

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 5537 (i.e. 74.411020689143). 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 $\frac{N}{d} = D$ )

5537 / 1 = 5537 (the remainder is 0, so 1 and 5537 are divisors of 5537)
5537 / 2 = 2768.5 (the remainder is 1, so 2 is not a divisor of 5537)
5537 / 3 = 1845.6666666667 (the remainder is 2, so 3 is not a divisor of 5537)
...
5537 / 73 = 75.849315068493 (the remainder is 62, so 73 is not a divisor of 5537)
5537 / 74 = 74.824324324324 (the remainder is 61, so 74 is not a divisor of 5537)