What are the divisors of 2355?

1, 3, 5, 15, 157, 471, 785, 2355

There is a total of 8 positive divisors.
The sum of these divisors is 3792.
The arithmetic mean is 474.

8 odd divisors

1, 3, 5, 15, 157, 471, 785, 2355

How to compute the divisors of 2355?

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 2355 by each of the numbers from 1 to 2355 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)

2355 / 1 = 2355 (the remainder is 0, so 1 is a divisor of 2355)
2355 / 2 = 1177.5 (the remainder is 1, so 2 is not a divisor of 2355)
2355 / 3 = 785 (the remainder is 0, so 3 is a divisor of 2355)
...
2355 / 2354 = 1.000424808836 (the remainder is 1, so 2354 is not a divisor of 2355)
2355 / 2355 = 1 (the remainder is 0, so 2355 is a divisor of 2355)

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 2355 (i.e. 48.528342234204). 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 $\frac{N}{d} = D$ )

2355 / 1 = 2355 (the remainder is 0, so 1 and 2355 are divisors of 2355)
2355 / 2 = 1177.5 (the remainder is 1, so 2 is not a divisor of 2355)
2355 / 3 = 785 (the remainder is 0, so 3 and 785 are divisors of 2355)
...
2355 / 47 = 50.106382978723 (the remainder is 5, so 47 is not a divisor of 2355)
2355 / 48 = 49.0625 (the remainder is 3, so 48 is not a divisor of 2355)