What are the divisors of 4465?

1, 5, 19, 47, 95, 235, 893, 4465

There is a total of 8 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 720.

8 odd divisors

1, 5, 19, 47, 95, 235, 893, 4465

How to compute the divisors of 4465?

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 4465 by each of the numbers from 1 to 4465 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)

4465 / 1 = 4465 (the remainder is 0, so 1 is a divisor of 4465)
4465 / 2 = 2232.5 (the remainder is 1, so 2 is not a divisor of 4465)
4465 / 3 = 1488.3333333333 (the remainder is 1, so 3 is not a divisor of 4465)
...
4465 / 4464 = 1.0002240143369 (the remainder is 1, so 4464 is not a divisor of 4465)
4465 / 4465 = 1 (the remainder is 0, so 4465 is a divisor of 4465)

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 4465 (i.e. 66.820655489152). 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 $\frac{N}{d} = D$ )

4465 / 1 = 4465 (the remainder is 0, so 1 and 4465 are divisors of 4465)
4465 / 2 = 2232.5 (the remainder is 1, so 2 is not a divisor of 4465)
4465 / 3 = 1488.3333333333 (the remainder is 1, so 3 is not a divisor of 4465)
...
4465 / 65 = 68.692307692308 (the remainder is 45, so 65 is not a divisor of 4465)
4465 / 66 = 67.651515151515 (the remainder is 43, so 66 is not a divisor of 4465)