What are the divisors of 2404?

1, 2, 4, 601, 1202, 2404

There is a total of 6 positive divisors.
The sum of these divisors is 4214.
The arithmetic mean is 702.33333333333.

4 even divisors

2, 4, 1202, 2404

2 odd divisors

1, 601

How to compute the divisors of 2404?

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 2404 by each of the numbers from 1 to 2404 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)

2404 / 1 = 2404 (the remainder is 0, so 1 is a divisor of 2404)
2404 / 2 = 1202 (the remainder is 0, so 2 is a divisor of 2404)
2404 / 3 = 801.33333333333 (the remainder is 1, so 3 is not a divisor of 2404)
...
2404 / 2403 = 1.0004161464836 (the remainder is 1, so 2403 is not a divisor of 2404)
2404 / 2404 = 1 (the remainder is 0, so 2404 is a divisor of 2404)

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 2404 (i.e. 49.030602688525). 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 $\frac{N}{d} = D$ )

2404 / 1 = 2404 (the remainder is 0, so 1 and 2404 are divisors of 2404)
2404 / 2 = 1202 (the remainder is 0, so 2 and 1202 are divisors of 2404)
2404 / 3 = 801.33333333333 (the remainder is 1, so 3 is not a divisor of 2404)
...
2404 / 48 = 50.083333333333 (the remainder is 4, so 48 is not a divisor of 2404)
2404 / 49 = 49.061224489796 (the remainder is 3, so 49 is not a divisor of 2404)