What are the divisors of 2388?

1, 2, 3, 4, 6, 12, 199, 398, 597, 796, 1194, 2388

There is a total of 12 positive divisors.
The sum of these divisors is 5600.
The arithmetic mean is 466.66666666667.

8 even divisors

2, 4, 6, 12, 398, 796, 1194, 2388

4 odd divisors

1, 3, 199, 597

How to compute the divisors of 2388?

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 2388 by each of the numbers from 1 to 2388 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)

2388 / 1 = 2388 (the remainder is 0, so 1 is a divisor of 2388)
2388 / 2 = 1194 (the remainder is 0, so 2 is a divisor of 2388)
2388 / 3 = 796 (the remainder is 0, so 3 is a divisor of 2388)
...
2388 / 2387 = 1.0004189359028 (the remainder is 1, so 2387 is not a divisor of 2388)
2388 / 2388 = 1 (the remainder is 0, so 2388 is a divisor of 2388)

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 2388 (i.e. 48.867166891482). 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 $\frac{N}{d} = D$ )

2388 / 1 = 2388 (the remainder is 0, so 1 and 2388 are divisors of 2388)
2388 / 2 = 1194 (the remainder is 0, so 2 and 1194 are divisors of 2388)
2388 / 3 = 796 (the remainder is 0, so 3 and 796 are divisors of 2388)
...
2388 / 47 = 50.808510638298 (the remainder is 38, so 47 is not a divisor of 2388)
2388 / 48 = 49.75 (the remainder is 36, so 48 is not a divisor of 2388)