What are the divisors of 4564?

1, 2, 4, 7, 14, 28, 163, 326, 652, 1141, 2282, 4564

There is a total of 12 positive divisors.
The sum of these divisors is 9184.
The arithmetic mean is 765.33333333333.

8 even divisors

2, 4, 14, 28, 326, 652, 2282, 4564

4 odd divisors

1, 7, 163, 1141

How to compute the divisors of 4564?

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 4564 by each of the numbers from 1 to 4564 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)

4564 / 1 = 4564 (the remainder is 0, so 1 is a divisor of 4564)
4564 / 2 = 2282 (the remainder is 0, so 2 is a divisor of 4564)
4564 / 3 = 1521.3333333333 (the remainder is 1, so 3 is not a divisor of 4564)
...
4564 / 4563 = 1.0002191540653 (the remainder is 1, so 4563 is not a divisor of 4564)
4564 / 4564 = 1 (the remainder is 0, so 4564 is a divisor of 4564)

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 4564 (i.e. 67.557383016218). 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 $\frac{N}{d} = D$ )

4564 / 1 = 4564 (the remainder is 0, so 1 and 4564 are divisors of 4564)
4564 / 2 = 2282 (the remainder is 0, so 2 and 2282 are divisors of 4564)
4564 / 3 = 1521.3333333333 (the remainder is 1, so 3 is not a divisor of 4564)
...
4564 / 66 = 69.151515151515 (the remainder is 10, so 66 is not a divisor of 4564)
4564 / 67 = 68.119402985075 (the remainder is 8, so 67 is not a divisor of 4564)