What are the divisors of 6032?

1, 2, 4, 8, 13, 16, 26, 29, 52, 58, 104, 116, 208, 232, 377, 464, 754, 1508, 3016, 6032

There is a total of 20 positive divisors.
The sum of these divisors is 13020.
The arithmetic mean is 651.

16 even divisors

2, 4, 8, 16, 26, 52, 58, 104, 116, 208, 232, 464, 754, 1508, 3016, 6032

4 odd divisors

1, 13, 29, 377

How to compute the divisors of 6032?

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 6032 by each of the numbers from 1 to 6032 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)

6032 / 1 = 6032 (the remainder is 0, so 1 is a divisor of 6032)
6032 / 2 = 3016 (the remainder is 0, so 2 is a divisor of 6032)
6032 / 3 = 2010.6666666667 (the remainder is 2, so 3 is not a divisor of 6032)
...
6032 / 6031 = 1.0001658099818 (the remainder is 1, so 6031 is not a divisor of 6032)
6032 / 6032 = 1 (the remainder is 0, so 6032 is a divisor of 6032)

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 6032 (i.e. 77.66595135579). 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 $\frac{N}{d} = D$ )

6032 / 1 = 6032 (the remainder is 0, so 1 and 6032 are divisors of 6032)
6032 / 2 = 3016 (the remainder is 0, so 2 and 3016 are divisors of 6032)
6032 / 3 = 2010.6666666667 (the remainder is 2, so 3 is not a divisor of 6032)
...
6032 / 76 = 79.368421052632 (the remainder is 28, so 76 is not a divisor of 6032)
6032 / 77 = 78.337662337662 (the remainder is 26, so 77 is not a divisor of 6032)