What are the divisors of 1582?

1, 2, 7, 14, 113, 226, 791, 1582

There is a total of 8 positive divisors.
The sum of these divisors is 2736.
The arithmetic mean is 342.

4 even divisors

2, 14, 226, 1582

4 odd divisors

1, 7, 113, 791

How to compute the divisors of 1582?

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 1582 by each of the numbers from 1 to 1582 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)

1582 / 1 = 1582 (the remainder is 0, so 1 is a divisor of 1582)
1582 / 2 = 791 (the remainder is 0, so 2 is a divisor of 1582)
1582 / 3 = 527.33333333333 (the remainder is 1, so 3 is not a divisor of 1582)
...
1582 / 1581 = 1.0006325110689 (the remainder is 1, so 1581 is not a divisor of 1582)
1582 / 1582 = 1 (the remainder is 0, so 1582 is a divisor of 1582)

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 1582 (i.e. 39.774363602703). 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 $\frac{N}{d} = D$ )

1582 / 1 = 1582 (the remainder is 0, so 1 and 1582 are divisors of 1582)
1582 / 2 = 791 (the remainder is 0, so 2 and 791 are divisors of 1582)
1582 / 3 = 527.33333333333 (the remainder is 1, so 3 is not a divisor of 1582)
...
1582 / 38 = 41.631578947368 (the remainder is 24, so 38 is not a divisor of 1582)
1582 / 39 = 40.564102564103 (the remainder is 22, so 39 is not a divisor of 1582)