What are the divisors of 4413?

1, 3, 1471, 4413

There is a total of 4 positive divisors.
The sum of these divisors is 5888.
The arithmetic mean is 1472.

4 odd divisors

1, 3, 1471, 4413

How to compute the divisors of 4413?

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 4413 by each of the numbers from 1 to 4413 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)

4413 / 1 = 4413 (the remainder is 0, so 1 is a divisor of 4413)
4413 / 2 = 2206.5 (the remainder is 1, so 2 is not a divisor of 4413)
4413 / 3 = 1471 (the remainder is 0, so 3 is a divisor of 4413)
...
4413 / 4412 = 1.0002266545784 (the remainder is 1, so 4412 is not a divisor of 4413)
4413 / 4413 = 1 (the remainder is 0, so 4413 is a divisor of 4413)

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 4413 (i.e. 66.430414720969). 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 $\frac{N}{d} = D$ )

4413 / 1 = 4413 (the remainder is 0, so 1 and 4413 are divisors of 4413)
4413 / 2 = 2206.5 (the remainder is 1, so 2 is not a divisor of 4413)
4413 / 3 = 1471 (the remainder is 0, so 3 and 1471 are divisors of 4413)
...
4413 / 65 = 67.892307692308 (the remainder is 58, so 65 is not a divisor of 4413)
4413 / 66 = 66.863636363636 (the remainder is 57, so 66 is not a divisor of 4413)