What are the divisors of 2316?

1, 2, 3, 4, 6, 12, 193, 386, 579, 772, 1158, 2316

There is a total of 12 positive divisors.
The sum of these divisors is 5432.
The arithmetic mean is 452.66666666667.

8 even divisors

2, 4, 6, 12, 386, 772, 1158, 2316

4 odd divisors

1, 3, 193, 579

How to compute the divisors of 2316?

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 2316 by each of the numbers from 1 to 2316 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)

2316 / 1 = 2316 (the remainder is 0, so 1 is a divisor of 2316)
2316 / 2 = 1158 (the remainder is 0, so 2 is a divisor of 2316)
2316 / 3 = 772 (the remainder is 0, so 3 is a divisor of 2316)
...
2316 / 2315 = 1.0004319654428 (the remainder is 1, so 2315 is not a divisor of 2316)
2316 / 2316 = 1 (the remainder is 0, so 2316 is a divisor of 2316)

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 2316 (i.e. 48.124837662064). 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 $\frac{N}{d} = D$ )

2316 / 1 = 2316 (the remainder is 0, so 1 and 2316 are divisors of 2316)
2316 / 2 = 1158 (the remainder is 0, so 2 and 1158 are divisors of 2316)
2316 / 3 = 772 (the remainder is 0, so 3 and 772 are divisors of 2316)
...
2316 / 47 = 49.276595744681 (the remainder is 13, so 47 is not a divisor of 2316)
2316 / 48 = 48.25 (the remainder is 12, so 48 is not a divisor of 2316)