What are the divisors of 4587?

1, 3, 11, 33, 139, 417, 1529, 4587

There is a total of 8 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 840.

8 odd divisors

1, 3, 11, 33, 139, 417, 1529, 4587

How to compute the divisors of 4587?

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 4587 by each of the numbers from 1 to 4587 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)

4587 / 1 = 4587 (the remainder is 0, so 1 is a divisor of 4587)
4587 / 2 = 2293.5 (the remainder is 1, so 2 is not a divisor of 4587)
4587 / 3 = 1529 (the remainder is 0, so 3 is a divisor of 4587)
...
4587 / 4586 = 1.0002180549498 (the remainder is 1, so 4586 is not a divisor of 4587)
4587 / 4587 = 1 (the remainder is 0, so 4587 is a divisor of 4587)

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 4587 (i.e. 67.727394752788). 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 $\frac{N}{d} = D$ )

4587 / 1 = 4587 (the remainder is 0, so 1 and 4587 are divisors of 4587)
4587 / 2 = 2293.5 (the remainder is 1, so 2 is not a divisor of 4587)
4587 / 3 = 1529 (the remainder is 0, so 3 and 1529 are divisors of 4587)
...
4587 / 66 = 69.5 (the remainder is 33, so 66 is not a divisor of 4587)
4587 / 67 = 68.462686567164 (the remainder is 31, so 67 is not a divisor of 4587)