What are the divisors of 2335?

1, 5, 467, 2335

There is a total of 4 positive divisors.
The sum of these divisors is 2808.
The arithmetic mean is 702.

4 odd divisors

1, 5, 467, 2335

How to compute the divisors of 2335?

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 2335 by each of the numbers from 1 to 2335 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)

2335 / 1 = 2335 (the remainder is 0, so 1 is a divisor of 2335)
2335 / 2 = 1167.5 (the remainder is 1, so 2 is not a divisor of 2335)
2335 / 3 = 778.33333333333 (the remainder is 1, so 3 is not a divisor of 2335)
...
2335 / 2334 = 1.0004284490146 (the remainder is 1, so 2334 is not a divisor of 2335)
2335 / 2335 = 1 (the remainder is 0, so 2335 is a divisor of 2335)

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 2335 (i.e. 48.321837713398). 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 $\frac{N}{d} = D$ )

2335 / 1 = 2335 (the remainder is 0, so 1 and 2335 are divisors of 2335)
2335 / 2 = 1167.5 (the remainder is 1, so 2 is not a divisor of 2335)
2335 / 3 = 778.33333333333 (the remainder is 1, so 3 is not a divisor of 2335)
...
2335 / 47 = 49.68085106383 (the remainder is 32, so 47 is not a divisor of 2335)
2335 / 48 = 48.645833333333 (the remainder is 31, so 48 is not a divisor of 2335)