What are the divisors of 1587?

1, 3, 23, 69, 529, 1587

There is a total of 6 positive divisors.
The sum of these divisors is 2212.
The arithmetic mean is 368.66666666667.

6 odd divisors

1, 3, 23, 69, 529, 1587

How to compute the divisors of 1587?

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 1587 by each of the numbers from 1 to 1587 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)

1587 / 1 = 1587 (the remainder is 0, so 1 is a divisor of 1587)
1587 / 2 = 793.5 (the remainder is 1, so 2 is not a divisor of 1587)
1587 / 3 = 529 (the remainder is 0, so 3 is a divisor of 1587)
...
1587 / 1586 = 1.000630517024 (the remainder is 1, so 1586 is not a divisor of 1587)
1587 / 1587 = 1 (the remainder is 0, so 1587 is a divisor of 1587)

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 1587 (i.e. 39.837168574084). 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 $\frac{N}{d} = D$ )

1587 / 1 = 1587 (the remainder is 0, so 1 and 1587 are divisors of 1587)
1587 / 2 = 793.5 (the remainder is 1, so 2 is not a divisor of 1587)
1587 / 3 = 529 (the remainder is 0, so 3 and 529 are divisors of 1587)
...
1587 / 38 = 41.763157894737 (the remainder is 29, so 38 is not a divisor of 1587)
1587 / 39 = 40.692307692308 (the remainder is 27, so 39 is not a divisor of 1587)