What are the divisors of 5533?

1, 11, 503, 5533

There is a total of 4 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 1512.

4 odd divisors

1, 11, 503, 5533

How to compute the divisors of 5533?

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 5533 by each of the numbers from 1 to 5533 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)

5533 / 1 = 5533 (the remainder is 0, so 1 is a divisor of 5533)
5533 / 2 = 2766.5 (the remainder is 1, so 2 is not a divisor of 5533)
5533 / 3 = 1844.3333333333 (the remainder is 1, so 3 is not a divisor of 5533)
...
5533 / 5532 = 1.0001807664497 (the remainder is 1, so 5532 is not a divisor of 5533)
5533 / 5533 = 1 (the remainder is 0, so 5533 is a divisor of 5533)

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 5533 (i.e. 74.384138094086). 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 $\frac{N}{d} = D$ )

5533 / 1 = 5533 (the remainder is 0, so 1 and 5533 are divisors of 5533)
5533 / 2 = 2766.5 (the remainder is 1, so 2 is not a divisor of 5533)
5533 / 3 = 1844.3333333333 (the remainder is 1, so 3 is not a divisor of 5533)
...
5533 / 73 = 75.794520547945 (the remainder is 58, so 73 is not a divisor of 5533)
5533 / 74 = 74.77027027027 (the remainder is 57, so 74 is not a divisor of 5533)