What are the divisors of 4586?

1, 2, 2293, 4586

There is a total of 4 positive divisors.
The sum of these divisors is 6882.
The arithmetic mean is 1720.5.

2 even divisors

2, 4586

2 odd divisors

1, 2293

How to compute the divisors of 4586?

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 4586 by each of the numbers from 1 to 4586 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)

4586 / 1 = 4586 (the remainder is 0, so 1 is a divisor of 4586)
4586 / 2 = 2293 (the remainder is 0, so 2 is a divisor of 4586)
4586 / 3 = 1528.6666666667 (the remainder is 2, so 3 is not a divisor of 4586)
...
4586 / 4585 = 1.0002181025082 (the remainder is 1, so 4585 is not a divisor of 4586)
4586 / 4586 = 1 (the remainder is 0, so 4586 is a divisor of 4586)

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 4586 (i.e. 67.720011813348). 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 $\frac{N}{d} = D$ )

4586 / 1 = 4586 (the remainder is 0, so 1 and 4586 are divisors of 4586)
4586 / 2 = 2293 (the remainder is 0, so 2 and 2293 are divisors of 4586)
4586 / 3 = 1528.6666666667 (the remainder is 2, so 3 is not a divisor of 4586)
...
4586 / 66 = 69.484848484848 (the remainder is 32, so 66 is not a divisor of 4586)
4586 / 67 = 68.44776119403 (the remainder is 30, so 67 is not a divisor of 4586)