What are the divisors of 2330?

1, 2, 5, 10, 233, 466, 1165, 2330

There is a total of 8 positive divisors.
The sum of these divisors is 4212.
The arithmetic mean is 526.5.

4 even divisors

2, 10, 466, 2330

4 odd divisors

1, 5, 233, 1165

How to compute the divisors of 2330?

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 2330 by each of the numbers from 1 to 2330 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)

2330 / 1 = 2330 (the remainder is 0, so 1 is a divisor of 2330)
2330 / 2 = 1165 (the remainder is 0, so 2 is a divisor of 2330)
2330 / 3 = 776.66666666667 (the remainder is 2, so 3 is not a divisor of 2330)
...
2330 / 2329 = 1.0004293688278 (the remainder is 1, so 2329 is not a divisor of 2330)
2330 / 2330 = 1 (the remainder is 0, so 2330 is a divisor of 2330)

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 2330 (i.e. 48.270073544589). 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 $\frac{N}{d} = D$ )

2330 / 1 = 2330 (the remainder is 0, so 1 and 2330 are divisors of 2330)
2330 / 2 = 1165 (the remainder is 0, so 2 and 1165 are divisors of 2330)
2330 / 3 = 776.66666666667 (the remainder is 2, so 3 is not a divisor of 2330)
...
2330 / 47 = 49.574468085106 (the remainder is 27, so 47 is not a divisor of 2330)
2330 / 48 = 48.541666666667 (the remainder is 26, so 48 is not a divisor of 2330)