What are the divisors of 5465?

1, 5, 1093, 5465

There is a total of 4 positive divisors.
The sum of these divisors is 6564.
The arithmetic mean is 1641.

4 odd divisors

1, 5, 1093, 5465

How to compute the divisors of 5465?

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 5465 by each of the numbers from 1 to 5465 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)

5465 / 1 = 5465 (the remainder is 0, so 1 is a divisor of 5465)
5465 / 2 = 2732.5 (the remainder is 1, so 2 is not a divisor of 5465)
5465 / 3 = 1821.6666666667 (the remainder is 2, so 3 is not a divisor of 5465)
...
5465 / 5464 = 1.0001830161054 (the remainder is 1, so 5464 is not a divisor of 5465)
5465 / 5465 = 1 (the remainder is 0, so 5465 is a divisor of 5465)

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 5465 (i.e. 73.925638313105). 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 $\frac{N}{d} = D$ )

5465 / 1 = 5465 (the remainder is 0, so 1 and 5465 are divisors of 5465)
5465 / 2 = 2732.5 (the remainder is 1, so 2 is not a divisor of 5465)
5465 / 3 = 1821.6666666667 (the remainder is 2, so 3 is not a divisor of 5465)
...
5465 / 72 = 75.902777777778 (the remainder is 65, so 72 is not a divisor of 5465)
5465 / 73 = 74.86301369863 (the remainder is 63, so 73 is not a divisor of 5465)