What are the divisors of 4467?

1, 3, 1489, 4467

There is a total of 4 positive divisors.
The sum of these divisors is 5960.
The arithmetic mean is 1490.

4 odd divisors

1, 3, 1489, 4467

How to compute the divisors of 4467?

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 4467 by each of the numbers from 1 to 4467 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)

4467 / 1 = 4467 (the remainder is 0, so 1 is a divisor of 4467)
4467 / 2 = 2233.5 (the remainder is 1, so 2 is not a divisor of 4467)
4467 / 3 = 1489 (the remainder is 0, so 3 is a divisor of 4467)
...
4467 / 4466 = 1.000223914017 (the remainder is 1, so 4466 is not a divisor of 4467)
4467 / 4467 = 1 (the remainder is 0, so 4467 is a divisor of 4467)

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 4467 (i.e. 66.835619246028). 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 $\frac{N}{d} = D$ )

4467 / 1 = 4467 (the remainder is 0, so 1 and 4467 are divisors of 4467)
4467 / 2 = 2233.5 (the remainder is 1, so 2 is not a divisor of 4467)
4467 / 3 = 1489 (the remainder is 0, so 3 and 1489 are divisors of 4467)
...
4467 / 65 = 68.723076923077 (the remainder is 47, so 65 is not a divisor of 4467)
4467 / 66 = 67.681818181818 (the remainder is 45, so 66 is not a divisor of 4467)