What are the divisors of 2312?

1, 2, 4, 8, 17, 34, 68, 136, 289, 578, 1156, 2312

There is a total of 12 positive divisors.
The sum of these divisors is 4605.
The arithmetic mean is 383.75.

9 even divisors

2, 4, 8, 34, 68, 136, 578, 1156, 2312

3 odd divisors

1, 17, 289

How to compute the divisors of 2312?

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 2312 by each of the numbers from 1 to 2312 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)

2312 / 1 = 2312 (the remainder is 0, so 1 is a divisor of 2312)
2312 / 2 = 1156 (the remainder is 0, so 2 is a divisor of 2312)
2312 / 3 = 770.66666666667 (the remainder is 2, so 3 is not a divisor of 2312)
...
2312 / 2311 = 1.0004327131112 (the remainder is 1, so 2311 is not a divisor of 2312)
2312 / 2312 = 1 (the remainder is 0, so 2312 is a divisor of 2312)

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 2312 (i.e. 48.083261120685). 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 $\frac{N}{d} = D$ )

2312 / 1 = 2312 (the remainder is 0, so 1 and 2312 are divisors of 2312)
2312 / 2 = 1156 (the remainder is 0, so 2 and 1156 are divisors of 2312)
2312 / 3 = 770.66666666667 (the remainder is 2, so 3 is not a divisor of 2312)
...
2312 / 47 = 49.191489361702 (the remainder is 9, so 47 is not a divisor of 2312)
2312 / 48 = 48.166666666667 (the remainder is 8, so 48 is not a divisor of 2312)