What are the divisors of 4583?

1, 4583

There is a total of 2 positive divisors.
The sum of these divisors is 4584.
The arithmetic mean is 2292.

2 odd divisors

1, 4583

How to compute the divisors of 4583?

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 4583 by each of the numbers from 1 to 4583 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)

4583 / 1 = 4583 (the remainder is 0, so 1 is a divisor of 4583)
4583 / 2 = 2291.5 (the remainder is 1, so 2 is not a divisor of 4583)
4583 / 3 = 1527.6666666667 (the remainder is 2, so 3 is not a divisor of 4583)
...
4583 / 4582 = 1.0002182453077 (the remainder is 1, so 4582 is not a divisor of 4583)
4583 / 4583 = 1 (the remainder is 0, so 4583 is a divisor of 4583)

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 4583 (i.e. 67.697858164051). 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 $\frac{N}{d} = D$ )

4583 / 1 = 4583 (the remainder is 0, so 1 and 4583 are divisors of 4583)
4583 / 2 = 2291.5 (the remainder is 1, so 2 is not a divisor of 4583)
4583 / 3 = 1527.6666666667 (the remainder is 2, so 3 is not a divisor of 4583)
...
4583 / 66 = 69.439393939394 (the remainder is 29, so 66 is not a divisor of 4583)
4583 / 67 = 68.402985074627 (the remainder is 27, so 67 is not a divisor of 4583)