What are the divisors of 2396?

1, 2, 4, 599, 1198, 2396

There is a total of 6 positive divisors.
The sum of these divisors is 4200.
The arithmetic mean is 700.

4 even divisors

2, 4, 1198, 2396

2 odd divisors

1, 599

How to compute the divisors of 2396?

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 2396 by each of the numbers from 1 to 2396 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)

2396 / 1 = 2396 (the remainder is 0, so 1 is a divisor of 2396)
2396 / 2 = 1198 (the remainder is 0, so 2 is a divisor of 2396)
2396 / 3 = 798.66666666667 (the remainder is 2, so 3 is not a divisor of 2396)
...
2396 / 2395 = 1.0004175365344 (the remainder is 1, so 2395 is not a divisor of 2396)
2396 / 2396 = 1 (the remainder is 0, so 2396 is a divisor of 2396)

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 2396 (i.e. 48.948953002082). 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 $\frac{N}{d} = D$ )

2396 / 1 = 2396 (the remainder is 0, so 1 and 2396 are divisors of 2396)
2396 / 2 = 1198 (the remainder is 0, so 2 and 1198 are divisors of 2396)
2396 / 3 = 798.66666666667 (the remainder is 2, so 3 is not a divisor of 2396)
...
2396 / 47 = 50.978723404255 (the remainder is 46, so 47 is not a divisor of 2396)
2396 / 48 = 49.916666666667 (the remainder is 44, so 48 is not a divisor of 2396)