What are the divisors of 1590?

1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795, 1590

There is a total of 16 positive divisors.
The sum of these divisors is 3888.
The arithmetic mean is 243.

8 even divisors

2, 6, 10, 30, 106, 318, 530, 1590

8 odd divisors

1, 3, 5, 15, 53, 159, 265, 795

How to compute the divisors of 1590?

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 1590 by each of the numbers from 1 to 1590 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)

1590 / 1 = 1590 (the remainder is 0, so 1 is a divisor of 1590)
1590 / 2 = 795 (the remainder is 0, so 2 is a divisor of 1590)
1590 / 3 = 530 (the remainder is 0, so 3 is a divisor of 1590)
...
1590 / 1589 = 1.0006293266205 (the remainder is 1, so 1589 is not a divisor of 1590)
1590 / 1590 = 1 (the remainder is 0, so 1590 is a divisor of 1590)

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 1590 (i.e. 39.874804074754). 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 $\frac{N}{d} = D$ )

1590 / 1 = 1590 (the remainder is 0, so 1 and 1590 are divisors of 1590)
1590 / 2 = 795 (the remainder is 0, so 2 and 795 are divisors of 1590)
1590 / 3 = 530 (the remainder is 0, so 3 and 530 are divisors of 1590)
...
1590 / 38 = 41.842105263158 (the remainder is 32, so 38 is not a divisor of 1590)
1590 / 39 = 40.769230769231 (the remainder is 30, so 39 is not a divisor of 1590)