What are the divisors of 2302?

1, 2, 1151, 2302

There is a total of 4 positive divisors.
The sum of these divisors is 3456.
The arithmetic mean is 864.

2 even divisors

2, 2302

2 odd divisors

1, 1151

How to compute the divisors of 2302?

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 2302 by each of the numbers from 1 to 2302 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)

2302 / 1 = 2302 (the remainder is 0, so 1 is a divisor of 2302)
2302 / 2 = 1151 (the remainder is 0, so 2 is a divisor of 2302)
2302 / 3 = 767.33333333333 (the remainder is 1, so 3 is not a divisor of 2302)
...
2302 / 2301 = 1.0004345936549 (the remainder is 1, so 2301 is not a divisor of 2302)
2302 / 2302 = 1 (the remainder is 0, so 2302 is a divisor of 2302)

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 2302 (i.e. 47.979162143581). 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 $\frac{N}{d} = D$ )

2302 / 1 = 2302 (the remainder is 0, so 1 and 2302 are divisors of 2302)
2302 / 2 = 1151 (the remainder is 0, so 2 and 1151 are divisors of 2302)
2302 / 3 = 767.33333333333 (the remainder is 1, so 3 is not a divisor of 2302)
...
2302 / 46 = 50.04347826087 (the remainder is 2, so 46 is not a divisor of 2302)
2302 / 47 = 48.978723404255 (the remainder is 46, so 47 is not a divisor of 2302)