What are the divisors of 2408?

1, 2, 4, 7, 8, 14, 28, 43, 56, 86, 172, 301, 344, 602, 1204, 2408

There is a total of 16 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 330.

12 even divisors

2, 4, 8, 14, 28, 56, 86, 172, 344, 602, 1204, 2408

4 odd divisors

1, 7, 43, 301

How to compute the divisors of 2408?

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 2408 by each of the numbers from 1 to 2408 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)

2408 / 1 = 2408 (the remainder is 0, so 1 is a divisor of 2408)
2408 / 2 = 1204 (the remainder is 0, so 2 is a divisor of 2408)
2408 / 3 = 802.66666666667 (the remainder is 2, so 3 is not a divisor of 2408)
...
2408 / 2407 = 1.0004154549231 (the remainder is 1, so 2407 is not a divisor of 2408)
2408 / 2408 = 1 (the remainder is 0, so 2408 is a divisor of 2408)

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 2408 (i.e. 49.071376585541). 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 $\frac{N}{d} = D$ )

2408 / 1 = 2408 (the remainder is 0, so 1 and 2408 are divisors of 2408)
2408 / 2 = 1204 (the remainder is 0, so 2 and 1204 are divisors of 2408)
2408 / 3 = 802.66666666667 (the remainder is 2, so 3 is not a divisor of 2408)
...
2408 / 48 = 50.166666666667 (the remainder is 8, so 48 is not a divisor of 2408)
2408 / 49 = 49.142857142857 (the remainder is 7, so 49 is not a divisor of 2408)