What are the divisors of 4582?

1, 2, 29, 58, 79, 158, 2291, 4582

There is a total of 8 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 900.

4 even divisors

2, 58, 158, 4582

4 odd divisors

1, 29, 79, 2291

How to compute the divisors of 4582?

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 4582 by each of the numbers from 1 to 4582 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)

4582 / 1 = 4582 (the remainder is 0, so 1 is a divisor of 4582)
4582 / 2 = 2291 (the remainder is 0, so 2 is a divisor of 4582)
4582 / 3 = 1527.3333333333 (the remainder is 1, so 3 is not a divisor of 4582)
...
4582 / 4581 = 1.0002182929491 (the remainder is 1, so 4581 is not a divisor of 4582)
4582 / 4582 = 1 (the remainder is 0, so 4582 is a divisor of 4582)

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 4582 (i.e. 67.690472003082). 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 $\frac{N}{d} = D$ )

4582 / 1 = 4582 (the remainder is 0, so 1 and 4582 are divisors of 4582)
4582 / 2 = 2291 (the remainder is 0, so 2 and 2291 are divisors of 4582)
4582 / 3 = 1527.3333333333 (the remainder is 1, so 3 is not a divisor of 4582)
...
4582 / 66 = 69.424242424242 (the remainder is 28, so 66 is not a divisor of 4582)
4582 / 67 = 68.388059701493 (the remainder is 26, so 67 is not a divisor of 4582)