What are the divisors of 2413?

1, 19, 127, 2413

There is a total of 4 positive divisors.
The sum of these divisors is 2560.
The arithmetic mean is 640.

4 odd divisors

1, 19, 127, 2413

How to compute the divisors of 2413?

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 2413 by each of the numbers from 1 to 2413 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)

2413 / 1 = 2413 (the remainder is 0, so 1 is a divisor of 2413)
2413 / 2 = 1206.5 (the remainder is 1, so 2 is not a divisor of 2413)
2413 / 3 = 804.33333333333 (the remainder is 1, so 3 is not a divisor of 2413)
...
2413 / 2412 = 1.0004145936982 (the remainder is 1, so 2412 is not a divisor of 2413)
2413 / 2413 = 1 (the remainder is 0, so 2413 is a divisor of 2413)

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 2413 (i.e. 49.122296363261). 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 $\frac{N}{d} = D$ )

2413 / 1 = 2413 (the remainder is 0, so 1 and 2413 are divisors of 2413)
2413 / 2 = 1206.5 (the remainder is 1, so 2 is not a divisor of 2413)
2413 / 3 = 804.33333333333 (the remainder is 1, so 3 is not a divisor of 2413)
...
2413 / 48 = 50.270833333333 (the remainder is 13, so 48 is not a divisor of 2413)
2413 / 49 = 49.244897959184 (the remainder is 12, so 49 is not a divisor of 2413)