What are the divisors of 4407?

1, 3, 13, 39, 113, 339, 1469, 4407

There is a total of 8 positive divisors.
The sum of these divisors is 6384.
The arithmetic mean is 798.

8 odd divisors

1, 3, 13, 39, 113, 339, 1469, 4407

How to compute the divisors of 4407?

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 4407 by each of the numbers from 1 to 4407 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)

4407 / 1 = 4407 (the remainder is 0, so 1 is a divisor of 4407)
4407 / 2 = 2203.5 (the remainder is 1, so 2 is not a divisor of 4407)
4407 / 3 = 1469 (the remainder is 0, so 3 is a divisor of 4407)
...
4407 / 4406 = 1.000226963232 (the remainder is 1, so 4406 is not a divisor of 4407)
4407 / 4407 = 1 (the remainder is 0, so 4407 is a divisor of 4407)

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 4407 (i.e. 66.385239323211). 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 $\frac{N}{d} = D$ )

4407 / 1 = 4407 (the remainder is 0, so 1 and 4407 are divisors of 4407)
4407 / 2 = 2203.5 (the remainder is 1, so 2 is not a divisor of 4407)
4407 / 3 = 1469 (the remainder is 0, so 3 and 1469 are divisors of 4407)
...
4407 / 65 = 67.8 (the remainder is 52, so 65 is not a divisor of 4407)
4407 / 66 = 66.772727272727 (the remainder is 51, so 66 is not a divisor of 4407)