What are the divisors of 5493?

1, 3, 1831, 5493

There is a total of 4 positive divisors.
The sum of these divisors is 7328.
The arithmetic mean is 1832.

4 odd divisors

1, 3, 1831, 5493

How to compute the divisors of 5493?

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 5493 by each of the numbers from 1 to 5493 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)

5493 / 1 = 5493 (the remainder is 0, so 1 is a divisor of 5493)
5493 / 2 = 2746.5 (the remainder is 1, so 2 is not a divisor of 5493)
5493 / 3 = 1831 (the remainder is 0, so 3 is a divisor of 5493)
...
5493 / 5492 = 1.0001820830299 (the remainder is 1, so 5492 is not a divisor of 5493)
5493 / 5493 = 1 (the remainder is 0, so 5493 is a divisor of 5493)

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 5493 (i.e. 74.114775854751). 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 $\frac{N}{d} = D$ )

5493 / 1 = 5493 (the remainder is 0, so 1 and 5493 are divisors of 5493)
5493 / 2 = 2746.5 (the remainder is 1, so 2 is not a divisor of 5493)
5493 / 3 = 1831 (the remainder is 0, so 3 and 1831 are divisors of 5493)
...
5493 / 73 = 75.246575342466 (the remainder is 18, so 73 is not a divisor of 5493)
5493 / 74 = 74.22972972973 (the remainder is 17, so 74 is not a divisor of 5493)