What are the divisors of 5485?

1, 5, 1097, 5485

There is a total of 4 positive divisors.
The sum of these divisors is 6588.
The arithmetic mean is 1647.

4 odd divisors

1, 5, 1097, 5485

How to compute the divisors of 5485?

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 5485 by each of the numbers from 1 to 5485 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)

5485 / 1 = 5485 (the remainder is 0, so 1 is a divisor of 5485)
5485 / 2 = 2742.5 (the remainder is 1, so 2 is not a divisor of 5485)
5485 / 3 = 1828.3333333333 (the remainder is 1, so 3 is not a divisor of 5485)
...
5485 / 5484 = 1.0001823486506 (the remainder is 1, so 5484 is not a divisor of 5485)
5485 / 5485 = 1 (the remainder is 0, so 5485 is a divisor of 5485)

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 5485 (i.e. 74.060785845142). 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 $\frac{N}{d} = D$ )

5485 / 1 = 5485 (the remainder is 0, so 1 and 5485 are divisors of 5485)
5485 / 2 = 2742.5 (the remainder is 1, so 2 is not a divisor of 5485)
5485 / 3 = 1828.3333333333 (the remainder is 1, so 3 is not a divisor of 5485)
...
5485 / 73 = 75.13698630137 (the remainder is 10, so 73 is not a divisor of 5485)
5485 / 74 = 74.121621621622 (the remainder is 9, so 74 is not a divisor of 5485)