What are the divisors of 4566?

1, 2, 3, 6, 761, 1522, 2283, 4566

There is a total of 8 positive divisors.
The sum of these divisors is 9144.
The arithmetic mean is 1143.

4 even divisors

2, 6, 1522, 4566

4 odd divisors

1, 3, 761, 2283

How to compute the divisors of 4566?

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 4566 by each of the numbers from 1 to 4566 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)

4566 / 1 = 4566 (the remainder is 0, so 1 is a divisor of 4566)
4566 / 2 = 2283 (the remainder is 0, so 2 is a divisor of 4566)
4566 / 3 = 1522 (the remainder is 0, so 3 is a divisor of 4566)
...
4566 / 4565 = 1.0002190580504 (the remainder is 1, so 4565 is not a divisor of 4566)
4566 / 4566 = 1 (the remainder is 0, so 4566 is a divisor of 4566)

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 4566 (i.e. 67.572183626105). 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 $\frac{N}{d} = D$ )

4566 / 1 = 4566 (the remainder is 0, so 1 and 4566 are divisors of 4566)
4566 / 2 = 2283 (the remainder is 0, so 2 and 2283 are divisors of 4566)
4566 / 3 = 1522 (the remainder is 0, so 3 and 1522 are divisors of 4566)
...
4566 / 66 = 69.181818181818 (the remainder is 12, so 66 is not a divisor of 4566)
4566 / 67 = 68.149253731343 (the remainder is 10, so 67 is not a divisor of 4566)