What are the divisors of 2411?

1, 2411

There is a total of 2 positive divisors.
The sum of these divisors is 2412.
The arithmetic mean is 1206.

2 odd divisors

1, 2411

How to compute the divisors of 2411?

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 2411 by each of the numbers from 1 to 2411 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)

2411 / 1 = 2411 (the remainder is 0, so 1 is a divisor of 2411)
2411 / 2 = 1205.5 (the remainder is 1, so 2 is not a divisor of 2411)
2411 / 3 = 803.66666666667 (the remainder is 2, so 3 is not a divisor of 2411)
...
2411 / 2410 = 1.0004149377593 (the remainder is 1, so 2410 is not a divisor of 2411)
2411 / 2411 = 1 (the remainder is 0, so 2411 is a divisor of 2411)

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 2411 (i.e. 49.101934788764). 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 $\frac{N}{d} = D$ )

2411 / 1 = 2411 (the remainder is 0, so 1 and 2411 are divisors of 2411)
2411 / 2 = 1205.5 (the remainder is 1, so 2 is not a divisor of 2411)
2411 / 3 = 803.66666666667 (the remainder is 2, so 3 is not a divisor of 2411)
...
2411 / 48 = 50.229166666667 (the remainder is 11, so 48 is not a divisor of 2411)
2411 / 49 = 49.204081632653 (the remainder is 10, so 49 is not a divisor of 2411)