What are the divisors of 2465?

1, 5, 17, 29, 85, 145, 493, 2465

There is a total of 8 positive divisors.
The sum of these divisors is 3240.
The arithmetic mean is 405.

8 odd divisors

1, 5, 17, 29, 85, 145, 493, 2465

How to compute the divisors of 2465?

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 2465 by each of the numbers from 1 to 2465 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)

2465 / 1 = 2465 (the remainder is 0, so 1 is a divisor of 2465)
2465 / 2 = 1232.5 (the remainder is 1, so 2 is not a divisor of 2465)
2465 / 3 = 821.66666666667 (the remainder is 2, so 3 is not a divisor of 2465)
...
2465 / 2464 = 1.0004058441558 (the remainder is 1, so 2464 is not a divisor of 2465)
2465 / 2465 = 1 (the remainder is 0, so 2465 is a divisor of 2465)

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 2465 (i.e. 49.648766349226). 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 $\frac{N}{d} = D$ )

2465 / 1 = 2465 (the remainder is 0, so 1 and 2465 are divisors of 2465)
2465 / 2 = 1232.5 (the remainder is 1, so 2 is not a divisor of 2465)
2465 / 3 = 821.66666666667 (the remainder is 2, so 3 is not a divisor of 2465)
...
2465 / 48 = 51.354166666667 (the remainder is 17, so 48 is not a divisor of 2465)
2465 / 49 = 50.30612244898 (the remainder is 15, so 49 is not a divisor of 2465)