What are the divisors of 5453?

1, 7, 19, 41, 133, 287, 779, 5453

There is a total of 8 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 840.

8 odd divisors

1, 7, 19, 41, 133, 287, 779, 5453

How to compute the divisors of 5453?

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 5453 by each of the numbers from 1 to 5453 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)

5453 / 1 = 5453 (the remainder is 0, so 1 is a divisor of 5453)
5453 / 2 = 2726.5 (the remainder is 1, so 2 is not a divisor of 5453)
5453 / 3 = 1817.6666666667 (the remainder is 2, so 3 is not a divisor of 5453)
...
5453 / 5452 = 1.0001834189288 (the remainder is 1, so 5452 is not a divisor of 5453)
5453 / 5453 = 1 (the remainder is 0, so 5453 is a divisor of 5453)

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 5453 (i.e. 73.844431069648). 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 $\frac{N}{d} = D$ )

5453 / 1 = 5453 (the remainder is 0, so 1 and 5453 are divisors of 5453)
5453 / 2 = 2726.5 (the remainder is 1, so 2 is not a divisor of 5453)
5453 / 3 = 1817.6666666667 (the remainder is 2, so 3 is not a divisor of 5453)
...
5453 / 72 = 75.736111111111 (the remainder is 53, so 72 is not a divisor of 5453)
5453 / 73 = 74.698630136986 (the remainder is 51, so 73 is not a divisor of 5453)