What are the divisors of 4401?

1, 3, 9, 27, 163, 489, 1467, 4401

There is a total of 8 positive divisors.
The sum of these divisors is 6560.
The arithmetic mean is 820.

8 odd divisors

1, 3, 9, 27, 163, 489, 1467, 4401

How to compute the divisors of 4401?

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 4401 by each of the numbers from 1 to 4401 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)

4401 / 1 = 4401 (the remainder is 0, so 1 is a divisor of 4401)
4401 / 2 = 2200.5 (the remainder is 1, so 2 is not a divisor of 4401)
4401 / 3 = 1467 (the remainder is 0, so 3 is a divisor of 4401)
...
4401 / 4400 = 1.0002272727273 (the remainder is 1, so 4400 is not a divisor of 4401)
4401 / 4401 = 1 (the remainder is 0, so 4401 is a divisor of 4401)

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 4401 (i.e. 66.340033162488). 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 $\frac{N}{d} = D$ )

4401 / 1 = 4401 (the remainder is 0, so 1 and 4401 are divisors of 4401)
4401 / 2 = 2200.5 (the remainder is 1, so 2 is not a divisor of 4401)
4401 / 3 = 1467 (the remainder is 0, so 3 and 1467 are divisors of 4401)
...
4401 / 65 = 67.707692307692 (the remainder is 46, so 65 is not a divisor of 4401)
4401 / 66 = 66.681818181818 (the remainder is 45, so 66 is not a divisor of 4401)