What are the divisors of 5454?

1, 2, 3, 6, 9, 18, 27, 54, 101, 202, 303, 606, 909, 1818, 2727, 5454

There is a total of 16 positive divisors.
The sum of these divisors is 12240.
The arithmetic mean is 765.

8 even divisors

2, 6, 18, 54, 202, 606, 1818, 5454

8 odd divisors

1, 3, 9, 27, 101, 303, 909, 2727

How to compute the divisors of 5454?

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 5454 by each of the numbers from 1 to 5454 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)

5454 / 1 = 5454 (the remainder is 0, so 1 is a divisor of 5454)
5454 / 2 = 2727 (the remainder is 0, so 2 is a divisor of 5454)
5454 / 3 = 1818 (the remainder is 0, so 3 is a divisor of 5454)
...
5454 / 5453 = 1.0001833852925 (the remainder is 1, so 5453 is not a divisor of 5454)
5454 / 5454 = 1 (the remainder is 0, so 5454 is a divisor of 5454)

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 5454 (i.e. 73.851201750547). 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 $\frac{N}{d} = D$ )

5454 / 1 = 5454 (the remainder is 0, so 1 and 5454 are divisors of 5454)
5454 / 2 = 2727 (the remainder is 0, so 2 and 2727 are divisors of 5454)
5454 / 3 = 1818 (the remainder is 0, so 3 and 1818 are divisors of 5454)
...
5454 / 72 = 75.75 (the remainder is 54, so 72 is not a divisor of 5454)
5454 / 73 = 74.712328767123 (the remainder is 52, so 73 is not a divisor of 5454)