What are the divisors of 3832?

1, 2, 4, 8, 479, 958, 1916, 3832

There is a total of 8 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 900.

6 even divisors

2, 4, 8, 958, 1916, 3832

2 odd divisors

1, 479

How to compute the divisors of 3832?

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 3832 by each of the numbers from 1 to 3832 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)

3832 / 1 = 3832 (the remainder is 0, so 1 is a divisor of 3832)
3832 / 2 = 1916 (the remainder is 0, so 2 is a divisor of 3832)
3832 / 3 = 1277.3333333333 (the remainder is 1, so 3 is not a divisor of 3832)
...
3832 / 3831 = 1.0002610284521 (the remainder is 1, so 3831 is not a divisor of 3832)
3832 / 3832 = 1 (the remainder is 0, so 3832 is a divisor of 3832)

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 3832 (i.e. 61.903150162169). 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 $\frac{N}{d} = D$ )

3832 / 1 = 3832 (the remainder is 0, so 1 and 3832 are divisors of 3832)
3832 / 2 = 1916 (the remainder is 0, so 2 and 1916 are divisors of 3832)
3832 / 3 = 1277.3333333333 (the remainder is 1, so 3 is not a divisor of 3832)
...
3832 / 60 = 63.866666666667 (the remainder is 52, so 60 is not a divisor of 3832)
3832 / 61 = 62.819672131148 (the remainder is 50, so 61 is not a divisor of 3832)