What are the divisors of 5458?

1, 2, 2729, 5458

There is a total of 4 positive divisors.
The sum of these divisors is 8190.
The arithmetic mean is 2047.5.

2 even divisors

2, 5458

2 odd divisors

1, 2729

How to compute the divisors of 5458?

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 5458 by each of the numbers from 1 to 5458 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)

5458 / 1 = 5458 (the remainder is 0, so 1 is a divisor of 5458)
5458 / 2 = 2729 (the remainder is 0, so 2 is a divisor of 5458)
5458 / 3 = 1819.3333333333 (the remainder is 1, so 3 is not a divisor of 5458)
...
5458 / 5457 = 1.0001832508704 (the remainder is 1, so 5457 is not a divisor of 5458)
5458 / 5458 = 1 (the remainder is 0, so 5458 is a divisor of 5458)

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 5458 (i.e. 73.878278269056). 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 $\frac{N}{d} = D$ )

5458 / 1 = 5458 (the remainder is 0, so 1 and 5458 are divisors of 5458)
5458 / 2 = 2729 (the remainder is 0, so 2 and 2729 are divisors of 5458)
5458 / 3 = 1819.3333333333 (the remainder is 1, so 3 is not a divisor of 5458)
...
5458 / 72 = 75.805555555556 (the remainder is 58, so 72 is not a divisor of 5458)
5458 / 73 = 74.767123287671 (the remainder is 56, so 73 is not a divisor of 5458)