What are the divisors of 2032?

1, 2, 4, 8, 16, 127, 254, 508, 1016, 2032

There is a total of 10 positive divisors.
The sum of these divisors is 3968.
The arithmetic mean is 396.8.

8 even divisors

2, 4, 8, 16, 254, 508, 1016, 2032

2 odd divisors

1, 127

How to compute the divisors of 2032?

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 2032 by each of the numbers from 1 to 2032 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)

2032 / 1 = 2032 (the remainder is 0, so 1 is a divisor of 2032)
2032 / 2 = 1016 (the remainder is 0, so 2 is a divisor of 2032)
2032 / 3 = 677.33333333333 (the remainder is 1, so 3 is not a divisor of 2032)
...
2032 / 2031 = 1.0004923682915 (the remainder is 1, so 2031 is not a divisor of 2032)
2032 / 2032 = 1 (the remainder is 0, so 2032 is a divisor of 2032)

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 2032 (i.e. 45.077710678339). 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 $\frac{N}{d} = D$ )

2032 / 1 = 2032 (the remainder is 0, so 1 and 2032 are divisors of 2032)
2032 / 2 = 1016 (the remainder is 0, so 2 and 1016 are divisors of 2032)
2032 / 3 = 677.33333333333 (the remainder is 1, so 3 is not a divisor of 2032)
...
2032 / 44 = 46.181818181818 (the remainder is 8, so 44 is not a divisor of 2032)
2032 / 45 = 45.155555555556 (the remainder is 7, so 45 is not a divisor of 2032)