What are the divisors of 4411?

1, 11, 401, 4411

There is a total of 4 positive divisors.
The sum of these divisors is 4824.
The arithmetic mean is 1206.

4 odd divisors

1, 11, 401, 4411

How to compute the divisors of 4411?

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 4411 by each of the numbers from 1 to 4411 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)

4411 / 1 = 4411 (the remainder is 0, so 1 is a divisor of 4411)
4411 / 2 = 2205.5 (the remainder is 1, so 2 is not a divisor of 4411)
4411 / 3 = 1470.3333333333 (the remainder is 1, so 3 is not a divisor of 4411)
...
4411 / 4410 = 1.0002267573696 (the remainder is 1, so 4410 is not a divisor of 4411)
4411 / 4411 = 1 (the remainder is 0, so 4411 is a divisor of 4411)

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 4411 (i.e. 66.415359669281). 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 $\frac{N}{d} = D$ )

4411 / 1 = 4411 (the remainder is 0, so 1 and 4411 are divisors of 4411)
4411 / 2 = 2205.5 (the remainder is 1, so 2 is not a divisor of 4411)
4411 / 3 = 1470.3333333333 (the remainder is 1, so 3 is not a divisor of 4411)
...
4411 / 65 = 67.861538461538 (the remainder is 56, so 65 is not a divisor of 4411)
4411 / 66 = 66.833333333333 (the remainder is 55, so 66 is not a divisor of 4411)